Director Doug Hamilton has made a film that will leave elaborate arrangements of Green Day songs in your head for days. Whether that prospect seems like the raddest thing ever or like some Dick Cheneyan enhanced interrogation technique is for you to decide. Note that the songs in question are from the band’s pissed-off 2004 political concept album, American Idiot. “I felt sort of validated as a songwriter,” says Billie Joe Armstrong, front man of the hugest Bay Area pop-punk trio ever, about becoming a Broadway sensation. He admits that he’s not supposed to admit that. It’s sweet. As the stage show evolved, via well-received workshopping at Berkeley Rep, Armstrong became more and more involved. Not that it was wholly out of left field, as vintage video of a wee Billie Joe singing “Send in the Clowns” tenderly suggests. As interviewed by Hamilton, he talks about Green Day’s priority-skewing success and the rarity of being in the special flow of creative collaboration with kindred spirits. “It didn’t happen in rock ‘n’ roll music, he says. “It happened in theater.” The arrangements, and the stagings, do tend to magnify punk-boilerplate cliches, and sometimes it is hard not to think this whole enterprise part of the terrible Hot Topicification of America. (Sample lyric, as a reminder: “She puts her makeup on like graffiti on the walls of the heartland.”) That said, it’s easy to see why American Idiot the Broadway show was such a smash.