Find the Area of the Specified Region $r ^ { 2 } = 4 \sin 2 \theta$

Multiple Choice

Find the area of the specified region.
-Inside the lemniscate $r ^ { 2 } = 4 \sin 2 \theta$ and outside the circle $r = \sqrt { 2 }$

A) $\frac { 2 } { 3 } ( 3 \sqrt { 3 } - \pi + 6 )$
B) $\frac { 4 \pi } { 3 }$
C) $\frac { 2 } { 3 } ( 3 \sqrt { 3 } - \pi )$
D) $\frac { 1 } { 2 } ( 2 \pi + 3 \sqrt { 3 } )$