ILL 1982 Problem 50

Let $O$ be the midpoint of the axis of a right circular cylinder. Let $A$ and $B$ be diametrically opposite points of one base, and $C$ a point of the other base circle that does not belong to the plane $OAB$ . Prove that the sum of dihedral angles of the trihedral $OABC$ is equal to $2\pi$ .