Which is greater $x_1$ or $x_2$?

We have

$$\frac{3}{5} > \frac{1}{2} \implies \arcsin \frac{3}{5} > \arcsin \frac{1}{2} = \frac{\pi}{6}$$

and

$$\frac{2\sqrt{2}}{3} > \frac{\sqrt{3}}{2} \implies \arcsin \frac{2\sqrt{2}}{3} > \arcsin \frac{\sqrt{3}}{2} = \frac{\pi}{3},$$

hence

$$x_2 > \frac{\pi}{6} + \frac{\pi}{3} = \frac{\pi}{2}.$$