Evaluate
\frac{\left(4\sqrt{3}-\pi \right)\left(-16\sqrt{3}\pi ^{3}+10752\pi \sqrt{3}+\pi ^{4}-1152\pi ^{2}+36864\right)}{12\left(-80\sqrt{3}\pi ^{3}+7680\pi \sqrt{3}+5\pi ^{4}-36864\right)}\approx 23.522542678
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