Given that $\alpha$ is an angle in the first quadrant, $\beta$ is an angle in the third quadrant, $\tan \alpha + \tan \beta = 4$, $\tan \alpha \tan \beta = \sqrt { 2 } + 1$, then $\sin ( \alpha + \beta ) =$ $\_\_\_\_$ .
$-\frac{2\sqrt{2}}{3}$
Given that $\alpha$ is an angle in the first quadrant, $\beta$ is an angle in the third quadrant, $\tan \alpha + \tan \beta = 4$, $\tan \alpha \tan \beta = \sqrt { 2 } + 1$, then $\sin ( \alpha + \beta ) =$ $\_\_\_\_$ .