Two Planes Through a Moving Point

As shown in the figure, in the cube $ABCD\text{-}A_1B_1C_1D_1$ with edge length $1$, a point $P$ moves on the segment $A_1B$. Let $l$ be the line of intersection of the plane $DD_1P$ and the plane $CC_1P$.

1. Prove that $l\parallel CC_1$.

2. Suppose $P$ is the point of the segment $A_1B$ with $A_1P=\dfrac{1}{4}A_1B$. Find the sine of the dihedral angle between the plane $DD_1P$ and the plane $CC_1P$.