# Inspired by Shivamani Patil

Geometry Level 4

$\Large \dfrac{\tan(x + 120^{\circ})}{\tan(x - 30^{\circ})} = \dfrac{11}{2}$

If $$x$$ is a solution to the above equation, and $$\cos(4x) = \dfrac{a}{b},$$ where $$a$$ and $$b$$ are positive coprime integers, then find $$a + b.$$

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