IMO Shortlist 1991 problem 18

Let $\alpha$ be a rational number with $0 < \alpha < 1$ and $\cos (3 \pi \alpha) + 2\cos(2 \pi \alpha) = 0$ . Prove that $\alpha = \frac {2}{3}$ .

Izvor: Međunarodna matematička olimpijada, shortlist 1991

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