Answer
$\frac{dy}{d\theta}=2\tan\theta$
Work Step by Step
$y=\ln{(\sec^2\theta})$
On differentiating both sides:
$\frac{dy}{d\theta}=\frac{d(\ln{(\sec^2\theta}))}{d\theta}$
$\frac{dy}{d\theta}=\frac{1}{\sec^2\theta}\frac{d({(\sec^2\theta}))}
{d\theta}$
$\frac{dy}{d\theta}=\frac{{(2\sec\theta\sec\theta\tan\theta})}{\sec^2\theta}={2\tan\theta}$
$\frac{dy}{d\theta}=2\tan\theta$
