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$\text{sos}(x)=\sin^2(x)-\cos^2(x) \\ \text{cin}(x)=\cos^2(x)-\sin^2(x)$

Let us define two new trigonometric identities as shown above.

For real $x$, find the minimum value of $2\text{sos}(x)\text{cin}(x)$.

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