$\tan4x=\sqrt 3,\qquad 0\leq x \lt \pi$
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