Answer
$\dfrac{3}{4}$
Work Step by Step
Let us consider:
$f(\theta)=\sin \theta$
We are given that $\theta=60^{\circ}$
We know form the unit circle that
$\sin (60^{\circ})=\sin (\dfrac{\pi}{3})=\dfrac{\sqrt 3}{2}$
Thus, we have: $[f(\theta)]^2=[\sin (60^{\circ})]^2
\\=[\sin\dfrac{\pi}{3}]^2 \\ =[\dfrac{\sqrt 3}{2}]^2 \\=\dfrac{3}{4}$