The value of the expression $(sinx + cosecx)^2 + (cosx + secx)^2 - (tanx + cotx)^2$ wherever defined is equal to

$\tan 2 \alpha \cdot \tan \left(30^{\circ}-\alpha\right)+\tan 2 \alpha \cdot \tan \left(60^{\circ}-\alpha\right)+\tan \left(60^{\circ}-\alpha\right) \cdot \tan \left(30^{\circ}-\alpha\right)$ is equal to

If $\cos x + \cos y - \cos (x + y) = \frac{3}{2}$,then

$\tan \frac{\pi}{5}+2 \tan \frac{2 \pi}{5}+4 \cot \frac{4 \pi}{5}$ is equal to

If $\tan \left(\frac{\pi}{9}\right), x, \tan \left(\frac{7 \pi}{18}\right)$ are in arithmetic progression and $\tan \left(\frac{\pi}{9}\right), y, \tan \left(\frac{5 \pi}{18}\right)$ are also in arithmetic progression,then $|x-2 y|$ is equal to:

If $\sin x \cosh y = \cos \theta$,$\cos x \sinh y = \sin \theta$ and $4 \tan x = 3$,then $\sinh^2 y =$