4. For which triples of numbers $(x ; y ; z)$, satisfying the system $\left\{\begin{array}{l}\sin 2 x-\sin 2 y=3(x-y) \\ \cos 3 x-\cos 3 z=4(x-z)\end{array}\right.$, does the expression $\frac{\sin x+\sin y}{2-\sin z}$ take its maximum possible value?
Answer: $\left(\frac{\pi}{2}+2 \pi n ; \frac{\pi}{2}+2 \pi n ; \frac{\pi}{2}+2 \pi n\right), n \in Z$.