Watch Lin-Manuel Miranda, James Corden in 'Crosswalk the Musical: Hair'

'Hamilton' creator joined 'Late Late Show' host for partially nude production of 1967 rock musical, staged at L.A. traffic light

Lin-Manuel Miranda joined James Corden on Thursday's 'Late Late Show' for a partially nude crosswalk production of 1967 rock musical 'Hair.'

James Corden recruited Hamilton creator-star Lin-Manuel Miranda to join his Crosswalk theater production of 1967 rock musical Hair, staged at an L.A. traffic light on Thursday's Late Late Show.

Despite being only vaguely familiar with the play's story ("It's hippie culture," he said. "I think there's a war. Or there's been a war.") and wildly jealous of Miranda's Broadway success, Corden led his small cast through the production's most famous songs.

Before the ramshackle musical, Corden hyped up his crew by introducing an enthused Miranda. "In a lot of ways, I feel like everything I've ever done has been leading up to this moment," the performer gushed. "In the seven years I was writing Hamilton, all I could think was, 'This is big enough. I might get on the crosswalk.' And now it's happened."

After a bizarre parking lot rehearsal – in which Corden suggested, to no avail, that they get in the Sixties mindset with a group orgy – they hit the streets, timing each song during traffic stops as commuters honked their horns in annoyance.

Despite the objections of "CBS and the state of California," Miranda and Corden got into character by stripping down for a nude rendition of the 5th Dimension's signature single, "The Age of Aquarius/Let the Sunshine In."

A wide-eyed Miranda ended the segment by praising Corden's vision. "When it's a red light for the cars," he said, "it's a green light for my soul."