$$\tan4x=\sqrt 3,\qquad 0\leq x \lt \pi$$
4 solutions: $$ \frac{\pi}{12}, \frac{\pi}{3}, \frac{7\pi}{12}, \frac{5\pi}{6}$$
or 3 solutions: $$ \frac{\pi}{12}, \frac{\pi}{3}, \frac{7\pi}{12}$$ (text suggested this and no clues about why $$\frac{5\pi}{6}$$ was excluded