If $\sin \theta + \text{cosec} \theta = 2$,then $\sin^2 \theta + \text{cosec}^2 \theta = $

For which value of $x$ is $\cos x > \sin x$,where $x \in \left( \frac{\pi}{2}, \frac{3\pi}{2} \right)$?

$\tan 81^{\circ}-\tan 63^{\circ}-\tan 27^{\circ}+\tan 9^{\circ}$ equals to

The value of $\sum_{k=1}^3 \cos ^2\left((2 k-1) \frac{\pi}{12}\right)$ is equal to

The value of $\sqrt{3} \cot 20^{\circ} - 4 \cos 20^{\circ}$ is equal to

Consider the following parametric equation of a curve: $x(\theta) = |\cos 4\theta| \cos \theta$ and $y(\theta) = |\cos 4\theta| \sin \theta$,where $0 \leq \theta \leq 2\pi$. Which one of the following graphs represents the curve?