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If $\theta = \frac{17 \pi}{3}$,then $(\tan \theta - \cot \theta) = \dots$

The expression $\frac{\tan(x - \frac{\pi}{2}) \cdot \cos(\frac{3\pi}{2} + x) - \sin^3(\frac{7\pi}{2} - x)}{\cos(x - \frac{\pi}{2}) \cdot \tan(\frac{3\pi}{2} + x)}$ simplifies to:

Let $\theta$ be an angle in the standard position such that the point $(-5, 12)$ lies on its terminal side. Then:

$\operatorname{Tanh}^{-1}(\sin \theta) =$

Prove that:
$2 \sin ^{2} \frac{\pi}{6}+\csc ^{2} \frac{7 \pi}{6} \cos ^{2} \frac{\pi}{3}=\frac{3}{2}$

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