Use identities to find values of the sine and cosine functions of the function for the angle measure.
$2 \theta$, given $\sin \theta=-\frac{\sqrt{6}}{7}$ and $\cos \theta> 0$
\[
\cos 2 \theta=
\]
(Use fractions or pi for any numbers in the expression.)

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Answer

So, the final answer is $\boxed{0.755}$.

Steps

Step 1 ：We are given that $\sin \theta = -\frac{\sqrt{6}}{7}$ and $\cos \theta > 0$.

Step 2 ：We know that the formula for cosine of double angle is given by: $\cos 2 \theta = 1 - 2 \sin^2 \theta$.

Step 3 ：Substitute $\sin \theta = -\frac{\sqrt{6}}{7}$ into the formula to find $\cos 2 \theta$.

Step 4 ：After calculation, we find that the value of $\cos 2 \theta$ is approximately 0.755.

Step 5 ：So, the final answer is $\boxed{0.755}$.