9.145. $\sqrt{3} \cos^{-2} x < 4 \tan x$.
$$
\begin{aligned}
& \frac{\sqrt{3}}{\cos ^{2} x}-\frac{4 \sin x}{\cos x}\frac{\sqrt{3}}{2}, \Leftrightarrow \frac{\pi}{3}+2 \pi n<2 x<\pi-\frac{\pi}{3}+2 \pi n, n \in Z \\
\cos x \neq 0
\end{aligned}\right. \\
& \frac{\pi}{6}+\pi n<x<\frac{\pi}{3}+\pi n, n \in Z \\
& \text { Answer: } x \in\left(\frac{\pi}{6}+\pi n ; \frac{\pi}{3}+\pi n\right), n \in Z
$$