Given a random sample $X_1, \dots, X_n$ from a distribution with density $f(x|\theta)$, suppose an estimator $\hat{\theta}_n$ satisfies $\sqrt{n}(\hat{\theta}_n - \theta) \xrightarrow{d} N(0, V(\theta))$. According to the Delta Method, what is the asymptotic distribution of $\sqrt{n}(\sin(\hat{\theta}_n) - \sin(\theta))$?