If $\cos^4 \theta −\sin^4 \theta = x$. Find $\cos^6 \theta − \sin^6 \theta $ in terms of $x$.

If $\cos^4 \theta −\sin^4 \theta = x$. Find $\cos^6 \theta −
\sin^6 \theta $ in terms of $x$.

Given $\cos^4 \theta −\sin^4 \theta = x$ , I've to find the value of
$\cos^6 \theta − \sin^6 \theta $ .
Here is what I did: $\cos^4 \theta −\sin^4 \theta = x$.
($\cos^2 \theta −\sin^2 \theta)(\cos^2 \theta +\sin^2 \theta) = x$
Thus ($\cos^2 \theta −\sin^2 \theta)=x$ , so $\cos 2\theta=x$ .
Now $x^3=(\cos^2 \theta −\sin^2 \theta)^3=\cos^6 \theta-\sin^6
\theta +3 \sin^4 \theta \cos^2 \theta -3 \sin^2 \theta \cos^4 \theta $
So if I can find the value of $3 \sin^4 \theta \cos^2 \theta -3 \sin^2
\theta \cos^4 \theta $ in terms of $x$ , the question is solved. But how
to do that ?