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Third degree polynomial with sin roots [ILL 1974]

Source:

January 2, 2011
algebrapolynomialcalculusintegrationtrigonometryalgebra proposed

Problem Statement

Determine an equation of third degree with integral coefficients having roots sin⁡π14,sin⁡5π14\sin \frac{\pi}{14}, \sin \frac{5 \pi}{14} and sin⁡−3π14.\sin \frac{-3 \pi}{14}.
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