Sextette soundtrack cassette?

I was under the impression that "Happy Birthday, 21" and the rejected Alice Cooper ballad "No Time for Tears" were the only songs from Sextette which were issued... But I just discovered a write-up on the film that states the press kit came with a cassette soundtrack (which I can only presume is pink!). I'm hardly an aficionado on West, so I'm hoping somebody who is one can either confirm or deny the existence of that tape (and perhaps offer a track listing)... cuz if it's real, it's my new mission in life to obtain a copy!