Система уравнений(тригонометрия)

{x+y=π
{sin(y)+sin(x)=1

{y=π-x
{sin(π-x)+sin(x)=1

$sin(\pi-x)+sin(x)=1\\sin(x)+sin(x)=1\\2sin(x)=1\\sin(x)=\frac{1}{2}\\x=(-1)^n*arcsin(\frac{1}{2})+\pi*n,\ n\in Z\\x=(-1)^n*\frac{\pi}{6}+\pi*n,\ n\in Z\\\\ \left \{ {{x=(-1)^n*\frac{\pi}{6}+\pi*n,\ n\in Z} \atop {y=\pi-(-1)^n*\frac{\pi}{6}-\pi*n,\ n\in Z}} \right. \\\left \{ {{x=(-1)^n*\frac{\pi}{6}+\pi*n,\ n\in Z} \atop {y=(-1)^{n+1}*\frac{\pi}{6}-\pi(n-1),\ n\in Z}} \right.$