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Trigonometric equality

Source: Singapore MO 2011 senior round 2 Q3

June 25, 2011

trigonometryalgebra proposedalgebra

Problem Statement

Find all positive integers

n

such that

\cos\frac{\pi}{n}\cos\frac{2\pi}{n}\cos\frac{3\pi}{n}=\frac{1}{n+1}