If ∫_π / 6^π / 4( cot (x-(π)/3) cot (x+(π)/3)+1) d x=α log_e (√ 3 -1), then 9 α^2 is equal to ____.

If $\displaystyle \int_{\pi / 6}^{\pi / 4}\left(\cot \left(x-\frac{\pi}{3}\right) \cot \left(x+\frac{\pi}{3}\right)+1\right) d x=\alpha \log _{\mathrm{e}}(\sqrt{3}-1)$, then $\displaystyle 9 \alpha^2$ is equal to $\displaystyle \_\_\_\_$.