Random Real Number Uniformly Distributed Between [0,1]

B (y) is linearly distributed between 0 and 1 (linear graph with y intercept of 0 and a slop of 1/1)

Theta Scattered = pi - d * ArcSin(b)

How would I use a random real number uniformly distributed between [0,1] (within unit area) to compute possible scattering angles?

Any help is appreciated.

I'm not sure I understand the question.What do you mean by "linearly distributed"? Are you just trying to pick a random angle in \(\displaystyle (0,\pi/4)\)?