Verifying the fraction

Background In my last post we worked through a probability problem under heavy duress. Three points chosen uniformly at random from a unit disk - what's the probability their circumcircle fits inside? After pages of Jacobians, angular integrals, and trig identities, I arrived at P = 2 / 5 . But I ended the post with some uncertainty: You wonder if you actually got the right answer. It was a nice…