\[\begin{array}{l} {\text{Вычислите:}} \hfill \\ \cos \frac{{2\pi }}{{31}}\cos \frac{{4\pi }}{{31}}\cos \frac{{8\pi }}{{31}}\cos \frac{{16\pi }}{{31}}\cos \frac{{32\pi }}{{31}}. \hfill \\ \end{array}\]