Решите системное уровнение x+y=pi/ 3 sinx+ siny= 1

Решите задачу:

$\left \{ {{x+y=\frac{\pi }{3} } \atop {Sinx+Siny=1}} \right.\\\\\left \{ {{x+y=\frac{\pi }{3}} \atop {2Sin\frac{x+y}{2}Cos\frac{x-y}{2} =1}} \right.\\\\\left \{ {{x+y=\frac{\pi }{3}} \atop {2Sin\frac{\pi }{6}Cos\frac{x-y}{2}=1}} \right.\\\\\left \{ {{x+y=\frac{\pi }{3} } \atop {Cos\frac{x-y}{2}=1 }} \right.\\\\\left \{ {{x+y=\frac{\pi }{3} } \atop {\frac{x-y}{2}=2\pi n}} \right.$

$+\left \{ {{x+y=\frac{\pi }{3} } \atop {x-y=4\pi n }} \right.\\-------\\\\2x=\frac{\pi }{3}+4\pi n,n\in Z\\\\x=\frac{\pi }{6}+2\pi n,n\in Z\\\\y=\frac{\pi }{3}-\frac{\pi }{6}-2\pi n\\\\y=\frac{\pi }{6}-2\pi n,n\in Z\\\\(\frac{\pi }{6} +2\pi n;\frac{\pi }{6}-2\pi n),n\in Z$