“What the fuck is he doing here?” asks hitherto well-behaved Green Day frontman Billie Joe Armstrong as Donald Trump arrives for the opening night of “American Idiot,” the Broadway hit improbably based on the punk-rock band’s 2004 concept album of the same name. A bemused question that others may well have asked of Armstrong himself, it’s one that neatly encapsulates the civil clash of worlds portrayed in Doug Hamilton’s engaging backstage doc “Broadway Idiot.” A straightforward account of the show’s journey from conception to rehearsal to Great White Way triumph, it effectively doubles as a traditional let’s-put-on-a-show musical in its own right, albeit one with heavier guitars. As with the show itself, then, the pic’s appeal extends well beyond the bracket of Green Day fans; ancillary prospects, following its limited theatrical release, look bright.

A snarling rock opera of sorts, fueled by Armstrong’s rancor over both his father’s death and the political paranoia of post-9/11 America, the Grammy-winning “American Idiot” album elevated Green Day from bratty pop rebels to broadly respected musicians. It’s fitting that, having already made over their image in the music world, the same album proved to be their ticket into the more genteel medium of musical theater. On the one hand, the transition made sense: Chronicling the travails of a frustrated small-town inhabitant, named Jesus of Suburbia, through dense songcraft, “Idiot” was always a highly narrative, melodrama-tinged piece. On the other, the band’s raucous sound, coupled with Armstrong’s recklessly atonal vocals, could hardly be further from show-tune territory.

The most compelling stretches of “Broadway Idiot,” then, reveal how those dueling aesthetics met in the middle, over the course of a lengthy rehearsal process to which Hamilton — a veteran of such TV institutions as “60 Minutes” and “American Masters,” here making his feature directing debut — was granted unusually extensive access, first in Berkeley before transferring to New York.

While the film features plenty of footage of propulsive public performances (including a thrilling collaboration between the cast and Green Day at the 2010 Grammy Awards that immediately predated the show’s Broadway debut), its trump card is its access to rough rehearsal-room experiments like the rearrangement of the band’s song “Last Night on Earth” into a hushed, Phil Spector-style soul number. Though the film paints an unreservedly rosy picture of the show’s development — if any creative disagreements surfaced along the way, they’ve been left in the editing suite — it’s still rare to see the nuts and bolts behind any stage musical, much less one this unorthodox, exposed quite so generously. The actual storyline of the musical is only revealed to viewers at the halfway mark; an earlier explanation might have added resonance to some of the film’s initial musical performances.

The unlikely but increasingly firm friendship between Armstrong and the show’s arch, elegant director Michael Mayer emerges as the film’s principal human dynamic, particularly as Mayer coaxes the reticent rocker into playing a key supporting role in the production. Armstrong’s bandmates and the show’s gifted ensemble — led by John Gallagher Jr., now recognizable as the star of acclaimed independent film “Short Term 12” — are comparatively backgrounded figures, though the impression of tightly knit teamwork is maintained throughout.

Tech package, including Dan Krauss’ bright, hi-def lensing and crisp sound recording of onstage and offstage action, is tidily televisual: It’s the show’s artistic virtuosity, rather than his own, that Hamilton is out to showcase.

Film Review: ‘Broadway Idiot’

<p>Reviewed at London Film Festival (Sonic), Oct. 11, 2013. (Also in SXSW Film Festival — 24 Beats Per Second.) Running time: <strong>81 MIN.</strong></p>

  • Production: <p>A FilmBuff release and presentation. (International sales: Cinetic Media, New York.) Produced by Ira Pittelman.</p>
  • Crew: <p>Directed by Doug Hamilton. Camera (color, HD), Dan Krauss; editor, Rob Tinworth; music, Green Day; sound, Doug Dunderdale, Jim Choi, Gabe Monts, Everett Wong, Rick Albright, Gabe Cyr, Luis Granados, Matt Geldoff; re-recording mixer, Greg McCleary.</p>
  • With: <p>Billie Joe Armstrong, Michael Mayer, Tom Kitt, Carmel Dean, Mike Dirnt, Tre Cool, John Gallagher, Jr., Rebecca Naomi Jones, Christina Sajous, Michael Esper, Stark Sands, Matt Caplan, Steven Hoggett, Christine Jones, Tony Vincent, Mary Faber, Adrienne Armstrong.</p>