Докажите справедливость равенства: cosп/7cos2п/7cos4п/7=-1/8

$cos\frac{\pi}{7}cos\frac{2\pi}{7}cos\frac{4\pi}{7}=$

умножим и поделим на $8sin\frac{\pi}{7}$

$cos\frac{\pi}{7}*cos\frac{2\pi}{7}*cos\frac{4\pi}{7}=\frac{8sin\frac{\pi}{7}*cos\frac{\pi}{7}*cos\frac{2\pi}{7}*cos\frac{4\pi}{7}}{8sin\frac{\pi}{7}}=\\ =\frac{4sin\frac{2\pi}{7}*cos\frac{2\pi}{7}*cos\frac{4\pi}{7}}{8sin\frac{\pi}{7}}=\frac{2sin\frac{4\pi}{7}*cos\frac{4\pi}{7}}{8sin\frac{\pi}{7}}=\frac{sin\frac{8\pi}{7}}{8sin\frac{\pi}{7}}=-\frac{sin\frac{\pi}{7}}{8sin\frac{\pi}{7}}=-\frac{1}{8}$