If $\sinh x=\tan A$, then $|\tanh x|=$

$$ \frac{\sinh (x+y)+\sinh (x-y)}{\cosh (x+y)-\cosh (x-y)}= $$

Let $\alpha$ be the period of $3 \sin \frac{\pi x}{3}-\cos \frac{\pi x}{2}+\tan \frac{\pi x}{4}, \beta$ be the period of $\sin ^2\left(\frac{\pi}{7}+\frac{x}{4}\right)-\sin ^2\left(\frac{\pi}{7}-\frac{x}{4}\right)$, and $\gamma$ be the period of $\cos ^4 x+\sin ^4 x$. Then, $\frac{\alpha \gamma}{\beta}=$

If $\theta$ does not lie in the second quadrant and $\tan \theta=\frac{-3}{4}$, then $\tan \frac{\theta}{2}+\sin 2 \theta=$