JEE Math Practice Question
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 $\left[-\frac{\pi}{4}, \frac{3 \pi}{4}\right]$?
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