TGenPhaseSpace question

Hello! My question is a little more general than only TGenPhaseSpace but here it goes: In many routines simulating a 2-body decay, I have seen that the azimuthal angle is taken randomly from a cos(\theta) uniform distribution [-1, 1], while \phi is taken from a uniform [0, 2\pi]. I don’t understand why we don’t take \theta uniform [-pi, pi]. Do I need to refresh my vector calculus? Sorry for the simplicity of my question but I am a newbie in a subject that really fascinates me (physics simulations). I would also appreciate any bibliography except the physics manuals of geant. Thank you in advance!

TGenPhaseSpace code is based on the GENBOD function (W515 from CERNLIB)
that uses the Raubold and Lynch method described at
F. James, Monte Carlo Phase Space, CERN 68-15 (1968)