Ordering Three Dihedral Angles in a Regular Tetrahedron

As shown in the figure, in a regular tetrahedron $ABCD$, points $P$, $Q$, $R$ lie on edges $AB$, $AD$, $AC$, respectively, with $AQ=QD$ and $\dfrac{AP}{PB}=\dfrac{CR}{RA}=\dfrac 12$. Let $\alpha$, $\beta$, $\gamma$ denote the plane angles of the dihedral angles $A\text{-}PQ\text{-}R$, $A\text{-}PR\text{-}Q$, $A\text{-}QR\text{-}P$, respectively. Determine, with proof, which of the following claims is true:

1. $\beta>\gamma>\alpha$ 2. $\gamma>\beta>\alpha$ 3. $\alpha>\gamma>\beta$ 4. $\alpha>\beta>\gamma$