The number of solutions of the equation $4 \cos 2 \theta \cos 3 \theta=\sec \theta$ in the interval $[0,2 \pi]$ is

$$ \tan \frac{2 \pi}{7} \cdot \tan \frac{4 \pi}{7}+\tan \frac{4 \pi}{7} \cdot \tan \frac{\pi}{7}+\tan \frac{\pi}{7} \cdot \tan \frac{2 \pi}{7}= $$

If $\sqrt{3} \cos \theta+\sin \theta>0$, then