You will be given a trivia clue, and the category it belongs to. You should answer with the best answer that belongs in the category and is described by the clue. For simplicity, answers should be in all lower cased letters.

Category: ENTERTAINMENT HISTORY 
Clue: Originally known as the Missouri Rockets, they performed at the opening of an East Coast theatre in 1931
the rockettes

Category: HISTORIC LASTS 
Clue: In the "thanks a lot, fellas" department, Mongolia was the last country to join this group--August 9, 1945
the allies

Category: MUSICAL THEATER 
Clue: A Hollywood venue was renovated & renamed the Aquarius Theater to host this musical in 1968

hair