As shown in the figure, in the triangular pyramid $P - A B C$, $A B \perp B C$, $A B = 2$, $B C = 2 \sqrt { 2 }$, $P B = P C = \sqrt { 6 }$. The midpoints of $BP$, $AP$, and $BC$ are $D$, $E$, and $O$ respectively. $A D = \sqrt { 5 } D O$. Point $F$ is on $AC$ such that $B F \perp A O$.\\
(1) Prove that $EF \parallel$ plane $BEF$.\\
(2) Prove that plane $A D O \perp$ plane $B E F$.\\
(3) Find the sine of the dihedral angle $D - A O - C$.