17. (12 points)\\
As shown in the figure, the rectangular prism $A B C D - A _ { 1 } B _ { 1 } C _ { 1 } D _ { 1 }$ has a square base $A B C D$. Point $E$ is on edge $A A _ { 1 }$, and $B E \perp E C _ { 1 }$.\\
\includegraphics[max width=\textwidth, alt={}, center]{e9c14d42-34be-4379-93d0-c3f95f9ac1b2-04_495_334_577_902}\\
(1) Prove that $B E \perp$ plane $E B _ { 1 } C _ { 1 }$;\\
(2) If $A E = A _ { 1 } E$, find the sine of the dihedral angle $B - E C - C _ { 1 }$.\\