In the unit cube $A B C D-A_{1} B_{1} C_{1} D_{1}$, point $E$ is on edge $A \Lambda_{1}$, and $A E=\frac{3-\sqrt{6}}{3}$. A plane $\alpha$ is constructed through points $E, C, D_{1}$. The dihedral angle between $\alpha$ and the face $D C C_{1} D_{1}$ is $\qquad$