In this paper (page 6) I'm reading, the author has a uniform random variable $\zeta$ which takes on values between 0 and 1. He computes
$ 2 \arccos( \sqrt{ 1 - \zeta } ) $
But isn't that the same as computing $2 \arccos( \sqrt{ \zeta } )$, since $\zeta$ is uniform on [0..1]? Or is there a reason he may be doing that I'm missing?