Решите систему {cos ( x + у ) = -1/2 {sin x + sin у = корень из 3

Решите задачу:

$\displaystyle \left \{ {{\cos (x+y)=-0.5} \atop {\sin x+\sin y=\sqrt{3}}} \right. \Rightarrow \left \{ {{x+y= \frac{2\pi}{3} } \atop {2\sin \frac{x+y}{2}\cos \frac{x-y}{2} =\sqrt{3} }} \right. \\ \\ \\ \left \{ {{x+y= \frac{2\pi}{3} } \atop {\sin \frac{\pi}{3}\cos \frac{x-y}{2}= \frac{ \sqrt{3} }{2} }} \right. \Rightarrow \left \{ {{x+y= \frac{2\pi}{3} } \atop {\cos \frac{x-y}{2} =1}} \right.$

$\displaystyle +\left \{ {{x+y= \frac{2 \pi }{3}} \atop {x-y=0 }} \right. \\ .\,\,\,\,\, \frac{}{2x=\frac{2 \pi }{3}} \\ \\ x=\frac{\pi }{3} +2 \pi n,n \in Z\\ \\ y=\frac{ \pi }{3} +2 \pi n,n \in Z$