$$\lim_{n \to \infty} \left[\frac{1}{n^2} \sec^2 \frac{1}{n^2} + \frac{2}{n^2} \sec^2 \frac{4}{n^2} + \ldots + \frac{1}{n^2} \sec^2 1\right]$$ equals

A

$$\frac{1}{2} \sec 1$$

B

$$\frac{1}{2} \text{cosec} \, 1$$

C

$$\tan 1$$

D

$$\frac{1}{2} \tan 1$$