Serway & Jewett — Conservation of Energy: Problem 37

As a prank, someone has balanced a pumpkin at the highest point of a grain silo. The silo is topped with a hemispherical cap that is frictionless when wet. The line from the center of curvature of the cap to the pumpkin makes an angle \(\theta_i = 0^{\circ}\) with the vertical. While you happen to be standing nearby in the middle of a rainy night, a breath of wind makes the pumpkin start sliding downward from rest. It loses contact with the cap when the line from the center of curvature of the hemisphere to the pumpkin makes a certain angle with the vertical. What is this angle?