Solve the system of equations: \[\begin{aligned} \sin y - \sin x &= x-y; &&\text{and}\\ \sin y - \sin z &= z-y; && \text{and}\\ x-y+z &= \pi. \end{aligned}\]
\(f(x)\) is an increasing function defined on the interval \([0, 1]\). It is known that the range of its values belongs to the interval \([0, 1]\). Prove that, for any natural \(N\), the graph of the function can be covered by \(N\) rectangles whose sides are parallel to the coordinate axes so that the area of each is \(1/N^2\). (In a rectangle we include its interior points and the points of its boundary).