What is the value of $$\frac{2(1 - \sin^2 \theta)\cosec^2 \theta}{\cot^2 \theta(1 + \tan^2 \theta)} - 1$$?

$$\frac{2(1-\sin^2\theta)\operatorname{cosec}^2\theta}{\cot^2\theta(1+\tan^2\theta)}-1\ .$$

$$=\frac{2\cos^2\theta\ \operatorname{cosec}^2\theta}{\frac{\cos^2\theta}{\sin^2\theta\ }.\sec^2\theta\ }-1\ .$$

$$=\frac{2\cos^2\theta\ \operatorname{cosec}^2\theta\sin^2\theta\ }{\cos^2\theta.\sec^2\theta\ }-1\ .$$

$$=\frac{2\ .\ 1.\ \ 1}{\sec^2\theta\ }-1\ .$$

$$=2\ \cos^2\theta\ -1\ .$$

$$=\cos2\theta\ \ .$$

D is correct choice.