17. (13 points)\\
As shown in the figure, $AA _ { 1 } \perp$ plane $ABC$, $BB _ { 1 } \parallel AA _ { 1 }$, $AB = AC = 3$, $BC = 2 \sqrt { 5 }$, $AA _ { 1 } = \sqrt { 7 }$, $BB _ { 1 } = 2 \sqrt { 7 }$. Points $E$ and $F$ are the midpoints of $BC$ and $A _ { 1 } C$ respectively.\\
(I) Prove that $EF \parallel$ plane $A _ { 1 } B _ { 1 } BA$;\\
(II) Prove that plane $AEA _ { 1 } \perp$ plane $BCB _ { 1 }$.\\
(III) Find the angle between line $A _ { 1 } B _ { 1 }$ and plane $BCB _ { 1 }$.\\
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