Given a circle, we choose 4 angles at random (uniformly distributed).
What are the chances that the four of them would be at the same half-circle ?
The way I thought about solving it, is to define to look at the segment $$[0,2\pi]$$ And define the first angle as $\theta_1=0$,
And then I reduced the question, to
"what is the probability of difference between the max and min being less than pi"
However, my approach is problematic when dealing the cyclic nature of the angle
I'd love to hear your ideas on how to approach this problem