Question bank/JEE Advanced/Mathematics

What is the value of

$$\sec ^{-1}\left(\frac{1}{4} \sum_{k=0}^{10} \sec \left(\frac{7 \pi}{12}+\frac{k \pi}{2}\right) \sec \left(\frac{7 \pi}{12}+\frac{(k+1) \pi}{2}\right)\right)$$

in the interval $\left[-\frac{\pi}{4}, \frac{3 \pi}{4}\right]$?

Source: JEEBench (IIT Delhi) / JEE Adv 2019 Paper 2