StarSolidStarSolidStarSolidStarSolid(4 stars)

I remember coming home from college one summer and talking politics with my father on our back porch; we must have been arguing about colonialism and the history of U.S. foreign intervention when I told him about a CIA-led coup in Iran in 1953 that overthrew Mohammad Mossadegh, the country’s democratically elected prime minister, and installed the far more compliant (and, it turned out, corrupt and tyrannical) Shah.

My father didn’t believe me, a harbinger of cultural and political reality-bubbles that would only harden over the subsequent forty years. But it did happen — on Aug. 19 of that year, as it happens — and in the absorbing, densely layered documentary “Coup 53,” not only are the events of that episode revisited with painfully precise detail, but some of their enduring mysteries are plumbed to tantalizingly provocative effect.

Traveling from Iran to Paris to London and Washington, filmmaker Taghi Amirani is on a mission simply to memorialize the coup, which turned out to be a joint effort of the United States and the United Kingdom to protect oil interests against Mossadegh’s nationalization of that industry. (He was reflexively — and wrongly — perceived as a natural ally of the U.S.S.R., even though he was a fervent anti-communist.)

Although the Americans eventually copped to their role in the coup — effectively taking credit for it — Britain has stayed mum about an event that launched a thousand tragic ripple effects, most notably the rise of Ayatollah Khomeini, who plunged a sophisticated, cosmopolitan country into miserable religious repression. As one source observes in “Coup 53,” Feb. 11, 1979 — the day the Ayatollah assumed power — was effectively Aug. 20, 1953.

In erasing their own fingerprints from Mossadegh’s removal, the U.K. also scrubbed from the record one of the event’s most important players, a shadowy figure named Norman Darbyshire. Following a trail that includes visits with Mossadegh’s family, poring over a trove of documents at Washington’s National Security Archive and discovering a gold mine in the form of an old television documentary, Arimani and editor Walter Murch transform “Coup 53” before our eyes from a personal essay to an illuminating political history and finally to a brilliantly self-referential exercise in documentary filmmaking (the Post-it notes that festoon the team’s office offer a candid glimpse of just how difficult seamlessness is to pull off).

At a time when “gaslighting” has taken pride of place in the collective vernacular, “Coup 53” offers an invaluable tutorial in how it’s been practiced, not just by awful individuals, but — perhaps even more dangerously — corporations and governments that hide greed, chauvinism and bareknuckled self-interest behind a scrim of moral righteousness and, in this case, Cold War paranoia.

As enlightening as “Coup 53” is as a secret history, it’s even more satisfying as an aesthetic exercise, treating viewers to one of cleverest workarounds in cinematic problem-solving in recent memory. It’s a nonfiction film that functions precisely as all documentaries should: as a piece of doggedly investigative, personally transparent reporting, and as simply great storytelling, full stop.

Unrated. Available at sunscinema.com and afisilver.afi.com. Contains nothing objectionable. In English, Farsi and French with subtitles. 118 minutes.