43

Part of 1970 IMO Longlists

Problems(1)

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

Source: IMO LongList 1970 - P43

Prove that the equation

x^3 - 3 \tan\frac{\pi}{12} x^2 - 3x + \tan\frac{\pi}{12}= 0

x_1 = \tan \frac{\pi}{36}

, and find the other roots.

trigonometryalgebra proposedalgebra