Answer
$2+\sqrt3$.
Work Step by Step
We know that $\cot(A/2)=\frac{\sin A}{1-\cos A}$.
Hence here $\cot \pi/12=\frac{\sin\pi/6}{1-\cos\pi/6}=\frac{0.5}{1-\frac{\sqrt3}{2}}=2+\sqrt3$.
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