Answer
$1$
Work Step by Step
$\lim_{\theta\to0}\frac{sin(sin\theta)}{\theta}=\lim_{\theta\to0}\frac{sin(sin\theta)}{sin\theta}\frac{sin\theta}{\theta}=\lim_{sin\theta\to0}\frac{sin(sin\theta)}{sin\theta}\lim_{\theta\to0}\frac{sin\theta}{\theta}=(1)(1)=1$