Answer
$2$
Work Step by Step
Here, we have $\lim\limits_{\theta \to 0} f(0)=\dfrac{0}{0}$
This shows an indeterminate form of limit, thus we will apply L-Hospital's rule such as:
$\lim\limits_{x \to \infty} f(x)=\lim\limits_{x \to \infty} \dfrac{p'(x)}{q'(x)}$
$\lim\limits_{\theta \to 0 \to 0} \dfrac{2 \sin^2 \theta}{\tan^2 \theta }=\dfrac{2 \sin^2 \theta}{\sin^2 \theta/\cos^2 \theta}$
Thus, $\lim\limits_{\theta \to 0} 2 \cos^2 \theta=2$
