Prove that: `cospi/7cos(2pi)/7cos(4pi)/7=-1/8,`

Explanation

`cos frac{pi}{7} cos frac{2pi}{7} cos frac{4pi}{7}=frac{1}{2 sin frac{pi}{7}(2 sin frac{2pi}{7} cos frac{2pi}{7}) cos frac{4pi}{7}`

`=frac{1}{2^2 sin frac{pi}{7}sin frac{8pi}{7}`

`=frac{1}{8}frac{sin(pi+frac{pi}{7})){sin frac{pi}{7}}=frac{1}{8}frac{-sin frac{pi}{7}}{sin frac{pi}{7}}=-frac{1}{8}`