Difficult Trigo

Geometry Level pending

If we have \[\tan\dfrac{\pi}{13}\tan\dfrac{2{\pi}}{13}\tan\dfrac{3{\pi}}{13}\cdots\tan\dfrac{6{\pi}}{13}=\dfrac {\sqrt{a}}{b}\] where \(\gcd(a,b)=1\), then find the value of \(a+b\).

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