Balancing a Semicircle Frame

Classical Mechanics Level 4

A semicircle with a constant mass per unit length is placed on a horizontal surface such that it doesn't topple in any direction. The touch point $P$ is assumed not to slip from the surface. Also, the imaginary line connecting the two end points of the semicircle forms an angle of $\theta$ with the surface.

Find the measure of $\theta$ (in degrees) to 2 decimal places.