import numpy as np

rng = np.random.default_rng()

x_dim = 7
y_dim = 7.3

d = 20.6 - 6.8 - 7 - 2.5

def generate_ray():
    x_start = rng.uniform(0, x_dim)
    y_start = rng.uniform(0, y_dim)

    phi = rng.uniform(0, 1) * 2 * np.pi
    theta = np.arccos(np.sqrt(rng.uniform(0, 1)))

    x_final = x_start + np.cos(phi) * d * np.tan(theta)
    y_final = y_start + np.sin(phi) * d * np.tan(theta)

    return (0 <= x_final and x_dim >= x_final and 0 <= y_final and y_dim >= y_final)


num = 1000000

count_in = 0 

for i in range(num):
    if generate_ray():
        count_in += 1
    

print(count_in)