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π/36 is a root of the equation - (Nice?)

Source: IMO LongList 1970 - P43

May 22, 2011
trigonometryalgebra proposedalgebra

Problem Statement

Prove that the equation x3−3tan⁡π12x2−3x+tan⁡π12=0x^3 - 3 \tan\frac{\pi}{12} x^2 - 3x + \tan\frac{\pi}{12}= 0 has one root x1=tan⁡π36x_1 = \tan \frac{\pi}{36}, and find the other roots.
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