How do you find the exact value of sin(arctan(2))?

Let $\alpha$ = arctan(2), then, we require the value of sin$\alpha$ . now tan $\alpha$ = 2$\implies$ sin$\alpha$ = 2/sqrt5.
tan$\alpha$ = 2 $\implies$ y= 2a, x = 2a & r = sqrt (5${a}^{2}$ ) = $\sqrt{5}$ a
sin$\alpha$ = 2a/ $\sqrt{5}$ a = 2/$\sqrt{5}$