Inspired by Shivamani Patil

Geometry Level 3

tan(x+120)tan(x30)=112 \dfrac{\tan(x + 120^{\circ})}{\tan(x - 30^{\circ})} = \dfrac{11}{2}

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

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