Too Easy (or too Difficult?)

Geometry Level 4

Determine the minimum value of

\(\frac{\sec^4\alpha}{\tan^2\beta}+\frac{\sec^4\beta}{\tan^2\alpha}\)

over all \(\alpha,\beta \neq \frac{k\pi}{2}\) where \(k\in\mathbb{Z}\).


Details and Assumptions:

\(\mathbb{Z}\) is the set of integers.

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