Find $\tan \beta$ from the given figure.

$\tan (\alpha + \beta) = 5/8$
 

$\tan (\alpha + \beta) = \dfrac{\tan \alpha + \tan \beta}{1 - \tan \alpha \, \tan \beta}$

$\dfrac{5}{8} = \dfrac{\frac{2}{8} + \tan \beta}{1 - \frac{2}{8}\tan \beta}$

$\frac{5}{8} - \frac{5}{32}\tan \beta = \frac{2}{8} + \tan \beta$

$\frac{3}{8} = \frac{37}{32} \tan \beta$

$\tan \beta = \frac{12}{37}$