If $\alpha$ be the bigger root of the equation $f(x)=ax^{2}-(4-2a)x-8=0$ where $a\in \left(\dfrac{4}{3}, 2\right)$ and if the value of $\cot^{-1}(2\tan\alpha)-\tan^{-1}\left(\dfrac{\cot\alpha}{2}\right)=2L$ then the value of $\dfrac{6L}{\pi}$ is

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