If \( \sin \alpha-\sin \beta=\frac{1}{3} \) and \( \cos \beta-\cos ...

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If \( \sin \alpha-\sin \beta=\frac{1}{3} \) and \( \cos \beta-\cos \alpha=\frac{1}{2} \), show that \( \cot \frac{\alpha+\beta}{2}=\frac{2}{3} \)
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