Equal Dihedral Traces

Let $M$ be the midpoint of edge $AD$ of a cube $ABCD\text{-}A_1B_1C_1D_1$ with edge length $2$, and let $P$ lie in the plane of face $BCC_1B_1$. If the plane $D_1PM$ makes equal acute dihedral angles with the planes $ABCD$ and $BCC_1B_1$, find the minimum distance from $P$ to $C_1$.