Recall the double angle identity:
[tex]\sin2\theta=2\sin\theta\cos\theta[/tex]
With [tex]\theta[/tex] measuring between 0º and 90º, we know [tex]\cos\theta>0[/tex]. So from the Pythagorean identity, we get
[tex]\sin^2\theta+\cos^2\theta=1\implies\cos\theta=\sqrt{1-\sin^2\theta}=\dfrac{\sqrt{21}}5[/tex]
Then
[tex]\sin2\theta=2\dfrac25\dfrac{\sqrt{21}}5=\dfrac{4\sqrt{21}}{25}[/tex]
