Uniform Angle Overlap

Question

Suppose that we have a unit circle sitting on the $(x,y)$ plane centered at $(0,0)$. We randomly generate an angle $\theta \sim \unif{0}{2\pi}$, and move along the perimeter of the circle $\theta$ radians counterclockwise from the point $(1,0)$, coloring the perimeter orange as we go. We then generate two more angles, $\alpha$ and $\beta$, independently from $\unif{0}{2\pi}$. An arc along the perimeter of the circle of length $\beta$ radians starting from the point that is $\alpha$ radians counterclockwise from $(1,0)$ is then colored green. What is the probability that the orange and green regions are disjoint?