# Alfaphication of Tan

Geometry Level pending

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 $$m+n$$.

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