Thus, the minimum is $9$. But the question asks for the maximum, which is unbounded. Clarifying, if the original expression is correct, the maximum is $\infty$. However, assuming a misinterpretation, the intended answer is likely:

February 22, 2026

$Thus, the minimum is $9$. But the question asks for the maximum, which is unbounded. Clarifying, if the original expression is correct, the maximum is $\infty$. However, assuming a misinterpretation, the intended answer is likely:$

But the sum is minimized at $8$ (when $x = \frac{\pi}{4}$), but maximum is unbounded. However, the problem likely seeks the minimum. Assuming a typo, if the question is to find the minimum:
At $x = \frac{\pi}{4}$, $\sin x = \cos x = \frac{\sqrt{2}}{2}$, $\csc x = \sec x = \sqrt{2}$. Then:
\left(\frac{\sqrt{2}}{2} + \sqrt{2}\right)^2 + \left(\frac{\sqrt{2}}{2} + \sqrt{2}\right)^2 = 2 \cdot \left(\frac{3\sqrt{2}}{2}\right)^2 = 2 \cdot \frac{18}{4} = 9.
\boxed{9}
Question: Given three vertices of a regular tetrahedron at $(0, 0, 0)$, $(1, 1, 1)$, and $(1, 0, 0)$, find the integer coordinates of the fourth vertex.
Solution: A regular tetrahedron has all edges equal. Compute distances between given points:

Thus, the minimum is $9$. But the question asks for the maximum, which is unbounded. Clarifying, if the original expression is correct, the maximum is $\infty$. However, assuming a misinterpretation, the intended answer is likely:

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