Answer
$$0$$
Work Step by Step
Given $$\lim_{\theta\to 0 }\frac{\sin^2 \theta }{\theta }$$
Then
\begin{align*}
\lim_{\theta\to 0 }\frac{\sin^2 \theta }{\theta }&= \lim_{\theta\to 0 }\sin \theta \frac{\sin \theta }{\theta } \\
&= \lim_{\theta\to 0 }[\sin \theta] \lim_{\theta\to 0 }\frac{\sin \theta }{\theta }\\
&=(0)(1)\\
&=0
\end{align*}