Simulate the angle between two vectors uniformly randomly picked in the unit square; see https://math.stackexchange.com/questions/3629474.

Question3629474.java

import java.util.Random;

public class Question3629474 {
    final static long ntrials = 100000000;
    final static Random random = new Random();
    
    public static void main(String [] args) {
        double sum = 0;
        for (long n = 0;n < ntrials;n++)
            sum += Math.abs(angle() - angle());
        System.out.println(sum / ntrials);
    }
    
    static double angle() {
        return (Math.atan2(random.nextDouble(), random.nextDouble()));
    }
}