$\begin{array}{l} D = \dfrac{1}{{\sin \dfrac{\pi }{7}}}\left( {2\cos \dfrac{\pi }{7}\sin \dfrac{{2\pi }}{7} + 2\cos \dfrac{{4\pi }}{7}\sin \dfrac{\pi }{7} + 2\cos \dfrac{{6\pi }}{7}\sin \dfrac{\pi }{7}} \right)\\ D = \dfrac{1}{{2\sin \dfrac{\pi }{7}}}\left( {\sin \dfrac{{3\pi }}{7} - \sin \dfrac{\pi }{7} + \sin \dfrac{{5\pi }}{7} - \sin \dfrac{{3\pi }}{7} + \sin \dfrac{{7\pi }}{7} - \sin \dfrac{{5\pi }}{7}} \right)\\ D = \dfrac{1}{{2\sin \dfrac{\pi }{7}}}\left( {\sin \pi - \sin \dfrac{\pi }{7}} \right) = \dfrac{1}{{2\sin \dfrac{\pi }{7}}}\left( {0 - \sin \dfrac{\pi }{7}} \right)\\ = \dfrac{{ - 1}}{2} \end{array}$
$\begin{array}{l} H = \cos \dfrac{\pi }{7} + \cos \dfrac{{3\pi }}{7} + \cos \dfrac{{5\pi }}{7}\\ H = \dfrac{1}{{2\sin \dfrac{\pi }{7}}}\left( {2\cos \dfrac{\pi }{7}\sin \dfrac{\pi }{7} + 2\cos \dfrac{{3\pi }}{7}\sin \dfrac{\pi }{7} + 2\cos \dfrac{{5\pi }}{7}\sin \dfrac{\pi }{7}} \right)\\ H = \dfrac{1}{{2\sin \dfrac{\pi }{7}}}\left( {\sin \dfrac{{2\pi }}{7} + \sin \dfrac{{4\pi }}{7} - \sin \dfrac{{2\pi }}{7} + \sin \dfrac{{6\pi }}{7} - \sin \dfrac{{4\pi }}{7}} \right)\\ H = \dfrac{{\sin \left( {\pi - \dfrac{\pi }{7}} \right)}}{{2\sin \dfrac{\pi }{7}}} = \dfrac{{\sin \dfrac{\pi }{7}}}{{2\sin \dfrac{\pi }{7}}} = \dfrac{1}{2} \end{array}$
