As shown in the figure, in the triangular pyramid $E - ABC$, plane $EAB \perp$ plane $ABC$, triangle $EAB$ is equilateral, $AC \perp BC$, and $AC = BC = \sqrt { 2 }$. $O$ and $M$ are the midpoints of $AB$ and $EA$ respectively.\n(1) Prove that $EB \parallel$ plane $MOC$.\n(2) Prove that plane $MOC \perp$ plane $EAB$.\n(3) Find the volume of the triangular pyramid $E - ABC$.