Let \( \mathrm{A} \) be an involuntary matrix and \( \mathrm{S} \) ...

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Let \( \mathrm{A} \) be an involuntary matrix and \( \mathrm{S} \) be the set containing solutions of \( \mathrm{A}^{\mathrm{x}}=\mathrm{I}, \mathrm{x}>0 \). The minimum value of \( \sum_{x \in S}^{\infty}\left(\sin ^{x} \theta+\cos ^{x} \theta\right) \)
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