If $\int \frac { \sin ^ { \frac { 3 } { 2 } } x + \cos ^ { \frac { 3 } { 2 } } x } { \sqrt { \sin ^ { 3 } x \cos ^ { 3 } x \sin ( x - \theta ) } } d x = A \sqrt { \cos \theta \tan x - \sin \theta } + B \sqrt { \cos \theta - \sin \theta \cot x } + C$, where $C$ is the integration constant, then $AB$ is equal to\\
(1) $4 \operatorname { cosec } ( 2 \theta )$\\
(2) $4 \sec \theta$\\
(3) $2 \sec \theta$\\
(4) $8 \operatorname { cosec } ( 2 \theta )$