$\cos \dfrac{\pi }{9} + \cos \dfrac{{2\pi }}{9} +  \ldots  + \cos \dfrac{{8\pi }}{9};$

${\sin ^2}\dfrac{\pi }{3} + {\sin ^2}\dfrac{\pi }{6} + {\sin ^2}\dfrac{\pi }{9} + {\sin ^2}\dfrac{{2\pi }}{9} + {\sin ^2}\dfrac{{5\pi }}{{18}} + {\sin ^2}\dfrac{{7\pi }}{{18}}$;

${\cos ^2}\dfrac{\pi }{3} + {\cos ^2}\dfrac{{5\pi }}{6} + {\cos ^2}\dfrac{\pi }{9} + {\cos ^2}\dfrac{{11\pi }}{{18}} + {\cos ^2}\dfrac{{13\pi }}{{18}} + {\cos ^2}\dfrac{{2\pi }}{9}$;

$\cos \dfrac{\pi }{5} + \cos \dfrac{{2\pi }}{5} +  \ldots  + \cos \dfrac{{9\pi }}{5};$

$\sin \dfrac{\pi }{5} + \sin \dfrac{{2\pi }}{5} +  \ldots  + \sin \dfrac{{9\pi }}{5}$