MathNet 2010 — Part 02 Question 166

The lengths of the nine edges of regular triangular prism $ABC-A_1B_1C_1$ are equal, $P$ is the midpoint of $CC_1$, and the dihedral angle $B-A_1P-B_1 = \alpha$. Then $\sin \alpha = \underline{\hspace{2cm}}$.