Решите пож систему уравнений

Решите задачу:

$\left \{ {{sinx+siny=\sqrt3} \atop {x+y=\pi }} \right. \; \left \{ {{sinx+sin(\pi -x)=\sqrt3} \atop {y=\pi -x}} \right. \; \left \{ {{2sinx=\sqrt3} \atop {y=\pi -x}} \right. \; \left \{ {{sinx=\frac{\sqrt3}{2}} \atop {y=\pi -x}} \right. \\\\ \left \{ {{x=(-1)^{n}\frac{\pi}{3}+\pi n,n\in Z} \atop {y=\pi -(-1)^{n}\frac{\pi}{3}-\pi n,n\in Z}} \right. \; \; \left \{ {{x=(-1)^{n}\frac {\pi}{3}+\pi n,\; n\in Z} \atop {y=(-1)^{n+1}\frac{\pi}{3}-\pi (n-1),\; n\in Z}} \right.$