One x, two x, three x

Geometry Level 3

If sinx=13cosx\sin {x} = -13\cos{x}. Then, the value of

sinx+sin2x+sin3xcosx+cos2x+cos3x\begin{aligned} \frac{\sin {x} + \sin{2x} + \sin{3x}}{\cos{x}+\cos{2x}+\cos{3x}} \end{aligned}

can be expressed in the form ab\frac{a}{b}, where aa and bb are positive coprime integers. What is the value of a+ba+b?

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