If costheta = 3/4, find the value of sin2theta

cos$\theta$ = $\frac 34$

$sin2\theta$ = $2sin\theta \times cos\theta$ = $2sin\theta \times \frac 34$ --- (i)

$sin^2 \theta$ = 1 - $cos^2 \theta$

$sin \theta$ = $\sqrt{1 - (\frac 34)^2}$ = $\frac {\sqrt7}{4}$

From (i),
$sin2\theta$ = $\frac{3\sqrt7}{8}$