8. 已知 $\tan \theta=\frac{3}{4}, \theta \in\left(\frac{\pi}{2}, \pi\right)$, 则 $\cos \left(\theta-\frac{\pi}{3}\right)$ 的值为 $-\frac{3 \sqrt{3}-4}{\underline{10}}$.
because \tan \theta=\frac{3}{4}, \therefore \sin \theta=\frac{3}{5}, \cos \theta=-\frac{4}{5}$,

$\therefore \cos \left(\theta-\frac{\pi}{3}\right)=\cos \theta \cos \frac{\pi}{3}+\sin \theta \sin \frac{\pi}{3}$

$=-\frac{4}{5} \times \frac{1}{2}+\frac{3}{5} \times \frac{\sqrt{3}}{2}=\frac{3 \sqrt{3}-4}{10}$.