UA-UMO 1999 Problem 113

All faces of a parallelepiped $ABCDA_1B_1C_1D_1$ are rhombi, and their angles at $A$ are all equal to $\alpha$ . Points $M,N,P,Q$ are selected on the edges $A_1B_1,DC,BC,A_1D_1$ , respectively, such that $A_1M=BP$ and $DN=A_1Q$ . Find the angle between the intersection lines of the plane $A_1BD$ with the planes $AMN$ and $APQ$ .