Expected Arc Length Between Random Points on a Sphere

Expectation · Medium · Free problem
Two points are chosen uniformly at random on the surface of the unit sphere in $\mathbb{R}^3$. Let $\theta$ be the great-circle (arc) distance between them, i.e., the central angle separating the two points, with $0 \le \theta \le \pi$. What is $E[\theta]$?

Open the full interactive solver, hints, and worked solution →