# a trigonometry problem

**Geometry**Level 4

\[\large \cos { (5x) } +\cos { (x) } +2\cos { (3x) } \sin { (2x) } =12\cos { (3x) } \]

If the solution of the equation above for \( 0<x<\dfrac { \pi }{ 2 } \) can be written as \(\dfrac { a }{ b } \pi \), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).