已知函数 $f(x)=\sin ^x \cos ^x-\cos ^2 x+\frac{1}{2}(x \in \mathbf{R})$. 若 $f\left(x_0\right)=\frac{3 \sqrt{2}}{10}, x_0 \in\left[\frac{\pi}{8}, \frac{3 \pi}{8}\right]$, 则 $\cos {2 x_0}=$
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