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

A

$$4\text{ cosec}(2\theta)$$

B

$$4\sec\theta$$

C

$$2\sec\theta$$

D

$$8\text{ cosec}(2\theta)$$