History barely remembers they were at Woodstock, as they were left out of the film due to contract issues. Their Grammy glory came the year before that awards show was recorded on videotape.

They played Vegas, the epitome of “selling out,” in their day. But there might have been a moment or two when Blood, Sweat & Tears was considered “cool.” They were founded by legendary musician, songwriter and session man Al Kooper, after all.

They were, at their peak (they’re still around) a nine-piece pop band with horns. Their sound was “ubiquitous” during a brief flash of time, between 1969-71. They’re remembered as part of a post-Janis Joplin/Joe Cocker Big Band rock era that included Chicago and The Electric Flag.

The Fifth Dimension and Three Dog Night were perhaps their closest analogs. BS&T was a singer-fronted “show band” whose original hits like “Spinning Wheel” were far outnumbered by jazzed-up covers of songs by the likes of Laura Nyro (“And When I Die”), Brenda Holloway and Berry Gordy (“You Make Me So Very Happy”) and The Beatles (“Got to Get You Into My Life”).

“What the Hell Happened to Blood, Sweat & Tears” is a documentary about a tipping point moment for the ensemble, when they took on a three nation State Dept.-sponsored tour of Eastern Europe at the height of the Vietnam War. They were the first pop band to play the role of “musical ambassadors” behind the Iron Curtain, something Louis Armstrong and jazz and classical music figures pioneered in the ’50s and ’60s.

“Selling out” to work for a government during a wildly unpopular war, they were condemned by the counter-culture, the underground press and eventually the mainstream press and their fanbase just as musical tastes moved on to glam, heavy metal, punk and disco.

But in their telling, they were “blackmailed” into committing career “suicide” by the Nixon Administration, which sought propaganda value — at home and abroad — from this “youth” group playing in Yugoslavia, Romania and Poland.

Writer-director John Scheinfeld, a veteran of historical music docs, is most famous for his “The U.S. vs. John Lennon” expose of government persecution of the most radical Beatle. He and his researchers have some receipts backing up that assertion in this film, memos from Henry Kissinger to Nixon, archived Romanian police state surveillance files and the like.

The story goes that singer David Clayton-Thomas, as distinct to their sound as their horns, had a police record in his native Canada and a fresh charge of threatening an ex-girlfriend with a gun (“Dropped,” he says). He faced deportation from the lucrative American market, or at the very least having his work visa yanked.

What makes that assertion credible is the Guess Who song “American Woman,” a tune whipped-up by that Canadian band when they were threatened with draft notices or deportation for overstaying their visas in the US during the Vietnam War.

But “blackmailed” into doing a three country State Dept. tour seems a stretch. What’s described here is a shady bit of “quid pro quo,” an ex-con manager “made a deal,” they got to continue touring and recording with their Canadian lead singer, IF they did this “favor” for the State Dept.

They’d come back, play Vegas and get labeled “uncool” and “sell-outs” and even picketed by Abbie Hoffman and others. That was the price of this “do us a favor we’ll do you a favor” “deal.”

BS&T brought a film crew along to capture their shows for a planned concert film, subject to State Dept. approval and dependent on whatever strictures the various governments in the countries where they were playing could think up. It never saw the light of day.

The film Scheinfeld got out of all of this political dealing, “James Bond” skullduggery and “Rocky and Bullwinkle/Peter Sellers” Cold War comedy is an account of a forgotten tour with moments of triumph, a near riot in Bucharest thanks to government goons and police dogs brought in to ensure that no one had too good of a time, and a night when BS&T bombed and were all but booed offstage in Zagreb.

So it’s a little bit “U.S. vs John Lennon,” and a hint of “Festival Express,” a doc about an infamous and ill-fated all-star Canadian rail tour on the heels of Woodstock.

Many band members remember the chilling moments mixed with thrills, being called-out for encore after encore, standing up to Romanian “decrees,” and seeing the consequences — kids arrested and beaten thanks to their concert.

A scholar from the Nixon presidential library provides Cold War context, actual concertgoers from Romania and Poland revel in the memories of this ground-breaking tour, and the band marvel at their reception — good and bad — in a part of the world where this sort of “rhythm” simply was not allowed.

Record label impresario Clive Davis provides musical judgement about what this interruption in their meteoric rise might have meant to their legacy and longevity.

And Rolling Stone writer David Felton shows up to read his snarky 1970 take on their return, a story headlined “BS&T Turns Backs on Commies,” and apologize for that and the blood-in-the-water rejection of a band which merely told people what they witnessed in the secretive Eastern Bloc — poverty and pitiless repression, not a popular stance with the West’s counter-culture of the day.

Critic David Wild might be closest to the mark in answering the “What the Hell Happened” question in describing their sound as making them a band “of their moment,” with less shelf life than the contemporaries who hewed to a guitar-quartet formula that evolved and endures as “classic rock.”

The film’s political focus seems a tad narrow, but the evidence that this tour — however it came to be — did them no favors and didn’t do Nixon any more service than his association with “Up With People” is convincing.

And hearing all the efforts filmmaker Donn Cambern and his traveling film crew went to in order to prevent Romanian destruction of their startling and historically-valuable footage makes one wish it could be recovered. What the State Dept. did to it stripped out that value and so muted the result that it’s just as well their edit never saw the light of day.

But if those 65 hours of concert, backstage and in-audience footage is around — just judging from the audio tape recordings of upset and irate band members backstage, outraged at Romanian police treatment of their audience — a fascinating and colorful piece of history has been lost and a generation far-removed from that era has been cheated of an eye-opening musical depiction of the Cold War at its ugly peak.

Rating: unrated

Cast: David Clayton-Thomas, Steve Katz, Fred Lipsius, Bobby Colomby, Tina Cunningham, Donn Cambern, David Wild, Jim Fielder, Tom Naftali, David Felton and Clive Davis

Credits: Scripted and directed by John Scheinfeld. An Abramorama release.

Running time: 1:52