Вычислить значение выражения: log32 sin(5pi\8)+log32 sin(6pi\8)+log32 sin(7pi\8)

Решите задачу:

$log_{32}(sin\frac{5\pi}{8})+log_{32}(sin\frac{6\pi}{8})+log_{32}\frac{7\pi}{8}=log_{32}(sin\frac{5\pi}{8}*sin\frac{7\pi}{8}*sin\frac{6\pi}{8})=\\=log_{32}(\frac{1}{2}(cos(\frac{5\pi}{8}-\frac{7\pi}{8})-cos(\frac{5\pi}{8}+\frac{7\pi}{8}))*sin\frac{3\pi}{4}=\\=log_{32}(\frac{1}{2}*(cos(-\frac{\pi}{4})-cos\frac{3\pi}{2})*sin(\pi-\frac{\pi}{4})=\\=log_{32}(\frac{1}{2}(\frac{\sqrt{2}}{2}-0)*sin\frac{\pi}{4}=log_{2^5}(\frac{\sqrt{2}}{4}*\frac{\sqrt{2}}{2})=\frac{1}{5}log_2\frac{1}{4}=\frac{1}{5}log_2(2)^{-2}=$
$=-\frac{2}{5}$