I've Invented New Trig!

Geometry Level 3

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

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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