chord intersection problem

chords.py

import math
import random

def random_angle():
    """Return a uniformly random angle on the unit circle."""
    return random.random() * 2 * math.pi

def chords_cross(a1, a2, b1, b2):
    """
    Return True if the chord from angle a1 to angle a2 crosses the chord from
    angle b1 to angle b2.
    """
    a1, a2 = sorted((a1, a2))
    b1, b2 = sorted((b1, b2))
    if a1 < b1:
        return a1 < b1 < a2 < b2
    else:
        return b1 < a1 < b2 < a2

def trial():
    a1, a2, b1, b2, c1, c2 = [random_angle() for i in range(6)]
    return (chords_cross(a1, a2, b1, b2) and
            chords_cross(a1, a2, c1, c2) and
            chords_cross(b1, b2, c1, c2))

trial_count = 100000
success_count = sum(trial() for i in range(trial_count))
print(f"experimental value after {trial_count} trials: {success_count / trial_count}")
print(f"theoretical value: {1/15}")

"""
$ python3 chords.py 
experimental value after 100000 trials: 0.06687
theoretical value: 0.06666666666666667
"""