[Euler-Fermat]

$\tan A = \frac{1}{7},\sin B = \frac{1}{\sqrt{10}}$
$A\in (0,\frac{\pi}{2}) ,B\in (0,\frac{\pi}{2})$
$\therefore \tan B =\frac{1}{3}$
$\tan 2B = \frac{\frac{2}{3}}{1-\frac{1}{9}} = \frac{3}{4}$
$\tan(A+2B) = 1 $
$A+2B \in (0,\frac{3\pi}{2})$
$\therefore A+2B = \frac{\pi}{4},\frac{5\pi}{4}$