The period of $|2\sin 3\theta + 4\cos 3\theta |$ is

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} = $

The period of $\sin \theta \cos \theta$ is

Let $f(x) = \cos px + \sin x$ be a periodic function,then $p$ must be

The period of $\left(\tan \theta - \frac{1}{3} \tan^3 \theta\right) \left(\frac{1}{3} - \tan^2 \theta\right)^{-1}$,where $\tan^2 \theta \neq \frac{1}{3}$,is

The period of $\tan(ky) + \sin(ky)$,where $k = 1 + 4 + 9 + \ldots$ ($20$ terms),is