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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