VMO 1962 Problem 4

Let be given a tetrahedron $ABCD$ such that triangle $BCD$ equilateral and $AB = AC = AD$ . The height is $h$ and the angle between two planes $ABC$ and $BCD$ is $\alpha$ . The point $X$ is taken on $AB$ such that the plane $XCD$ is perpendicular to $AB$ . Find the volume of the tetrahedron $XBCD$ .