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sin pi/18 .... sin 9pi/18

Source: Polish MO Finals 1976 p1

August 23, 2024

trigonometry

Problem Statement

Is the number

\sin \frac{\pi}{18} \sin \frac{3\pi}{18} \sin \frac{5\pi}{18} \sin \frac{7\pi}{18} \sin \frac{9\pi}{18}

rational?