\[\begin{array}{l} {\text{Докажите}}{\text{, что}} \hfill \\ {\sin ^4}\frac{\pi }{{16}} + {\sin ^4}\frac{{3\pi }}{{16}} + {\sin ^4}\frac{{5\pi }}{{16}} + {\sin ^4}\frac{{7\pi }}{{16}} = \frac{3}{2}. \hfill \\ \end{array}\]