Solution (source code)

= Solution

Stationarity requires both first <partial derivatives> to vanish:
$$
z_x=-\sin x\sin y=0,\qquad z_y=\cos x\cos y=0.
$$
For example, choosing $x=\pi$ and $\cos y=0$ gives two points strictly inside the prescribed rectangle:
$$
\boxed{(x,y)=(\pi,\pi/2),\qquad(\pi,3\pi/2)}.
$$
Both satisfy the two <derivative> equations directly.