If \( \sin (\alpha+\beta)=1 \) and \( \sin (\alpha-\beta)=\frac{1}{2} \), where \( 0 \leq \alpha...

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If \( \sin (\alpha+\beta)=1 \) and \( \sin (\alpha-\beta)=\frac{1}{2} \), where \( 0 \leq \alpha, \beta \leq \frac{\pi}{2} \), then find the values of \( \tan (\alpha+2 \beta) \) and \( \tan (2 \alpha+\beta) \).
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