3. Let $\alpha, \beta \in(0, \pi), \cos \alpha, \cos \beta$ be the roots of the equation $5 x^{2}-3 x-1=0$, then the value of $\sin \alpha \sin \beta$ is $\qquad$
$$
\begin{array}{l}
\left\{\begin{array}{l}
\cos \alpha + \cos \beta = \frac{3}{5}, \\
\cos \alpha \cos \beta = -\frac{1}{5}
\end{array} \Rightarrow \cos^2 \alpha + \cos^2 \beta = (\cos \alpha + \cos \beta)^2 - 2 \cos \alpha \cos \beta = \frac{19}{25}\right. \\
\Rightarrow \sin^2 \alpha \sin^2 \beta = \left(1 - \cos^2 \alpha\right)\left(1 - \cos^2 \beta\right) = 1 - \left(\cos^2 \alpha + \cos^2 \beta\right) + \cos^2 \alpha \cos^2 \beta \\
= 1 - \frac{19}{25} + \frac{1}{25} = \frac{7}{25} \text{, and } \alpha, \beta \in (0, \pi) \text{, so } \sin \alpha \sin \beta = \frac{\sqrt{7}}{5} \text{. } \\
\end{array}
$$