\[\begin{array}{l} {\text{Докажите тождества:}} \hfill \\ {\text{а) }}\sum\limits_{k = 1}^3 {\sqrt[3]{{{{\left( {\frac{{\cos \frac{{\pi k}}{7}}}{{\cos \frac{{2\pi k}}{7}}}} \right)}^2}}}} = \sqrt[3]{{49}};{\text{ б) }}\sum\limits_{k = 1}^3 {\sqrt[3]{{{{\left( {\frac{{\cos \frac{{2\pi k}}{7}}}{{\cos \frac{{\pi k}}{7}}}} \right)}^2}}}} = 2\sqrt[3]{7}; \hfill \\ {\text{в) }}\sum\limits_{k = 1}^4 {\sqrt[3]{{{{\left( {\frac{{\cos \frac{{\pi k}}{9}}}{{\cos \frac{{2\pi k}}{9}}}} \right)}^2}}}} = 2\sqrt[3]{9} + 1;{\text{ г) }}\sum\limits_{k = 1}^4 {\sqrt[3]{{{{\left( {\frac{{\cos \frac{{2\pi k}}{9}}}{{\cos \frac{{\pi k}}{9}}}} \right)}^2}}}} = 3\sqrt[3]{3} + 1. \hfill \\ \end{array}\]