Comparing Three Angles in a Folded Rectangle

In rectangle $ABCD$ with $AD<CD$, triangle $ACD$ is folded up along $AC$ to triangle $ACD_1$, so that the dihedral angle $A\text{-}CD_1\text{-}B$ is acute. Let $\alpha$ be the angle between lines $AD_1$ and $BC$, let $\beta$ be the angle between line $BD_1$ and plane $ABC$, and let $\gamma$ be the dihedral angle $A\text{-}CD_1\text{-}B$. Determine, with proof, the size relationship among $\alpha,\beta,\gamma$.