lean_workbook_plus_35079

Multiply with $\sin \left ( \frac{\pi}{7} \right ) \cdot \sin \left ( \frac{2\pi}{7} \right ) \cdot \sin \left ( \frac{3\pi}{7} \right )$ . And use $\sin u \cdot \sin v = \frac{1}{2} \cos (u-v) - \frac{1}{2} \cos (u+v)$ , to obtain the equivalent statement: \n$\cos \frac{\pi}{7} - \cos \frac{5\pi}{7} = \cos \frac{\pi}{7} - \cos \frac{3\pi}{7} + \cos \frac{2\pi}{7} - \cos \frac{4\pi}{7}$