2. The coordinates $(x ; y)$ of points in the square $\{(x ; y):-\pi \leq x \leq 2 \pi, 0 \leq y \leq 3 \pi\}$ satisfy the system of equations $\left\{\begin{array}{l}\sin x+\sin y=\sin 3 \\ \cos x+\cos y=\cos 3\end{array}\right.$. Find the coordinates $(x ; y)$ of all such points.
Answer: 1) five points;

$$
\text { 2) }\left\{\begin{array}{l}
x_{1}=3-\frac{\pi}{3} \\
y_{1}=3+\frac{\pi}{3}
\end{array} ;\left\{\begin{array}{l}
x=3-\frac{5 \pi}{3} \\
y=3+\frac{5 \pi}{3}
\end{array} ;\left\{\begin{array}{l}
x_{1}=3-\frac{5 \pi}{3} \\
y_{1}=3-\frac{\pi}{3}
\end{array} ;\left\{\begin{array}{l}
x_{1}=3+\frac{\pi}{3} \\
y_{1}=3-\frac{\pi}{3}
\end{array} ;\left\{\begin{array}{l}
x_{1}=3+\frac{\pi}{3} \\
y_{1}=3+\frac{5 \pi}{3}
\end{array} .\right.\right.\right.\right.\right.
$$