Let X, Y two random (uniform) points from the circle $x^{2} + y^{2} = 1$. What if the distribution of an angle between these points?
My try: To generate the point X from the circle $x^2 + y^2 = 1$ is the same, that generate angle $\theta_{X} \sim $ Uniform[$0, 2\pi$] and than taking $X = (\cos \theta_{X}, \sin \theta_{X})$. Than angle between X and Y is $max(\theta_{X}, \theta_{Y}) - \min(\theta_{X}, \theta_{Y})$