Вычислить:cos(пи/5)+cos(2пи/5)+cos(4пи/5)+cos(6пи/5)

$cos(\frac{\pi}{5}) + cos(\frac{2\pi}{5}) + cos(\frac{4\pi}{5})+cos(\frac{6\pi}{5})=\\\\ 2cos\frac{7\pi}{10}*cos\frac{\pi}{2} +cos\frac{2\pi}{5}+cos\frac{4\pi}{5}=\\\\ \frac{2sin\frac{2\pi}{5} (cos\frac{2\pi}{5}+cos\frac{4\pi}{5})}{2sin\frac{2\pi}{5}} =\\\\ sin\frac{4\pi}{5}+sin\frac{6\pi}{5}-sin\frac{2\pi}{5} = -sin\frac{2\pi}{5}\\\\ \frac{-sin\frac{2\pi}{5}}{2sin\frac{2\pi}{5}} = - \frac{1}{2}$