# 1 Trillion Followers Problem

Geometry Level 5

$\large \begin{cases}{\sin(2x) + \sin(2y) = 1/3} \\ {\cos(2x) + \cos(2y) = 5/7}\end{cases}$

Given $$x,y$$ satisfy the system of equations above, and denote the value of $$\tan(x) + \tan(y)$$ as $$\frac ab$$ for coprime positive integers $$a,b$$.

Find the value of $$a+b$$.

Bonus: For the general system of equations below, state $$\tan(x) + \tan(y)$$ in terms of $$A$$ and $$B$$.

$\large \begin{cases}{\sin(2x) + \sin(2y) = A} \\ {\cos(2x) + \cos(2y) = B}\end{cases}$

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