2. The coordinates $(x ; y)$ of points in the square $\{(x ; y):-2 \pi \leq x \leq 3 \pi,-\pi \leq y \leq 4 \pi\}$ satisfy the system of equations $\left\{\begin{array}{l}\sin x+\sin y=\sin 4 \\ \cos x+\cos y=\cos 4\end{array}\right.$. How many such points are there? Find the coordinates $(x ; y)$ of the points with the greatest abscissa.
Answer: 1) 13 points; 2) $\left\{\begin{array}{l}x=4+\frac{5 \pi}{3} \\ y=4+\frac{\pi}{3}\end{array} ;\left\{\begin{array}{l}x=4+\frac{5 \pi}{3} \\ y=4+\frac{7 \pi}{3}\end{array} ;\left\{\begin{array}{l}x=4+\frac{5 \pi}{3} \\ y=4-\frac{5 \pi}{3}\end{array}\right.\right.\right.$