Answer
$\frac{\sqrt{5}}{3}.$
Work Step by Step
Assume that $\sin\theta =\frac{2}{3}$, then by solving the triangle, we have:
$$\cos \theta=\frac{\sqrt{5}}{3}.$$
Now, since $\theta =\sin^{-1}\frac{2}{3}$, we have
$$\cos(\sin^{-1}\frac{2}{3})=\cos\theta=\frac{\sqrt{5}}{3}.$$
