Alfaphication of Tan

If we are given $\cot { \alpha } =\frac { 1 }{ 2 } ,\sec { \beta } =\frac { -5 }{ 3 }$ for $\pi <\alpha <\frac { 3\pi }{ 2 } ,\frac { \pi }{ 2 } <\beta <\pi$ . Then let $\tan { (\alpha +\beta )=\varsigma }$ and $p$ equals to the number of quadrant in which $\alpha +\beta$ terminates. If $\varsigma +p=\frac { m }{ n }$ for coprime integers $m$ and $n$ .Find $m+n$ .