Answer
$$J'(\theta)=2n\tan(n\theta)\sec^2(n\theta)$$
Work Step by Step
$$J'(\theta)=(\tan^2(n\theta))'=2\tan(n\theta)(\tan(n\theta))'=2\tan(n\theta)\frac{1}{\cos^2(n\theta)}(n\theta)'=
2\tan(n\theta)\frac{1}{\cos^2(n\theta)}\cdot n=2n\tan(n\theta)\sec^2(n\theta)$$
