Find out the central angle of the circle sector.

If the length of its arc is equal to the perimeter of

the circunference inscribed in it(circle sector).

The problem above complete radian answer(not in function of any variables)

I could set the answer in funcion of the central angle=$\displaystyle \theta$, and is:

$\displaystyle \theta (\csc\theta+1)=\pi$

Any suggest would be appretiated.