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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