Answer
$\dfrac{\sqrt 3}{2}$
Work Step by Step
Let us consider:
$f(\theta)=\sin \theta$
When $\theta=60^{\circ}$, then $2 \theta=2 (60^{\circ})=124^{\circ}$
We know from the unit circle that
$\sin (120^{\circ})=\sin (\dfrac{2\pi}{3})=\dfrac{\sqrt 3}{2}$
Thus, we have: $f(2\theta)=\sin (120^{\circ})
\\=\sin\dfrac{2\pi}{3} \\ =\dfrac{\sqrt 3}{2}$
