If $\displaystyle f(x,y) = sin x+ siny + sin (x+y)$, $\displaystyle 0\le x\le2\pi$, $\displaystyle 0\le y \le 2\pi$, find the extremum of $\displaystyle f$.

I find $\displaystyle f_x $and $\displaystyle f_y$ and equate them to zero. Then from these two equations, I get $\displaystyle cos x= cos y$.

Can anyone help me to proceed from here to get the extremum?