For \(\alpha, \beta \in(0, \frac{\pi} {2})\), let \(3 \sin (\alpha+\beta)=2 \sin (\alpha-\beta)\) and a real number \(k\…

For \(\alpha, \beta \in(0, \frac{\pi} {2})\), 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