IMO 1967 - Longlist Problems Question 21

(HUN 2) Without using any tables, find the exact value of the product $$P=\cos\frac\pi{15}\cos\frac{2\pi}{15}\cos\frac{3\pi}{15}\cos\frac{4\pi}{15}\cos\frac{5\pi}{15}\cos\frac{6\pi}{15}\cos\frac{7\pi}{15}.$$