The value of $$cosecθ secθ( \frac{1+sinθ}{cosθ} - \frac{cosθ}{1+sinθ}) - 2tan^{2}θ$$

Expression : $$cosecθ secθ( \frac{1+sinθ}{cosθ} - \frac{cosθ}{1+sinθ}) - 2tan^{2}θ$$

= $$cosec \theta sec \theta (\frac{(1 + sin \theta)^2 - cos^2 \theta}{cos \theta (1 + sin \theta)}) - 2tan^2 \theta$$

= $$\frac{1 + sin^2 \theta + 2sin \theta - cos^2 \theta}{cos^2 \theta (sin \theta + sin^2 \theta)} - 2tan^2 \theta$$

= $$\frac{2sin^2 \theta + 2sin \theta}{cos^2 \theta (sin \theta + sin^2 \theta)} - 2tan^2 \theta$$

= $$\frac{2}{cos^2 \theta} - 2tan^2 \theta$$

= $$2sec^2 \theta - 2tan^2 \theta$$

= $$2 (sec^2 \theta - tan^2 \theta) = 2 * 1 = 2$$