5. On the plane, there is a set of points $M$, the coordinates $X$ and $y$ of which are related by the equation

$$
\sin (x+2 y)=\sin x+\sin 2 y
$$

A circle of radius $R$, located on the same plane, does not intersect with the set $M$.

What values can the radius of such a circle take
Answer: $R \in\left(0 ; \frac{3-\sqrt{5}}{2} \pi\right)$