Find $\displaystyle {\tan{{\left(\alpha+\beta\right)}}}$ exactly, given $\displaystyle {\sec{\alpha}}=-\frac{{9}}{{2}}$ and $\displaystyle {\sin{\beta}}=-\frac{{1}}{{6}}$ where $\displaystyle \alpha$ terminates in quadrant II and $\displaystyle \beta$ terminates in quadrant IV. Be sure to reduce your final result completely.