Hi @ippo232. It is a nice problem.
The problem is the same, no matter which reference place we choose. So, we can think about these three circles.

The circumference in black has equation

the circunference in red has equation

and the circunference in green has equation

The shaded areas are equal in size, that is, just calculate the area of one and multiply it by three.

So making use of

we have that the shaded area is

.

I repeat, it is a nice problem.
Greetings from Venezuela