7. If $\cot \alpha=2, \tan (\alpha-\beta)=-\frac{2}{5}$, then the value of $\tan (\beta-2 \alpha)$ is
7. $-\frac{1}{12}$.
$\cot \alpha=2$, then $\tan \alpha=\frac{1}{2}, \tan (\beta-\alpha)=\frac{2}{5}$, then $\tan (\beta-2 \alpha)=\tan [(\beta-\alpha)-\alpha]=$ $\frac{\frac{2}{5}-\frac{1}{2}}{1+\frac{2}{5} \cdot \frac{1}{2}}=-\frac{1}{12}$