PL-OM 2014 Problem 3

A tetrahedron $ABCD$ with acute-angled faces is inscribed in a sphere with center $O$ . A line passing through $O$ perpendicular to plane $ABC$ crosses the sphere at point $D'$ that lies on the opposide side of plane $ABC$ than point $D$ . Line $DD'$ crosses plane $ABC$ in point $P$ that lies inside the triangle $ABC$ . Prove, that if $\angle APB=2\angle ACB$ , then $\angle ADD'=\angle BDD'$ .