# Should I use Triple Angle...

Geometry Level pending

The sum of all solutions to the equation

$$\cos 3x+\cos 7x+\cos 11x=0$$

over the interval $$[0, \pi]$$ can be expressed in the form $$\frac{a\pi}{b}$$, where $$a$$ and $$b$$ are positive coprime integers. What is the value of $$ab$$?

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