If \( \sin (A+B)=\cos (A-B)=\frac{\sqrt{3}}{2} \), then \( \cot 2 A \) \( = \)

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If \( \sin (A+B)=\cos (A-B)=\frac{\sqrt{3}}{2} \), then \( \cot 2 A \) \( = \)
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