Question
For $\alpha, \beta \in(0, \pi / 2)$, let $3 \sin (\alpha+\beta)=2 \sin (\alpha-\beta)$ and a real number $k$ be such that $\tan \alpha=k \tan \beta$. Then, the value of $k$ is equal to
For $\alpha, \beta \in(0, \pi / 2)$, let $3 \sin (\alpha+\beta)=2 \sin (\alpha-\beta)$ and a real number $k$ be such that $\tan \alpha=k \tan \beta$. Then, the value of $k$ is equal to