Solve this equation for $x\in (0,\frac{\pi}{2})$

$\mathrm{cos}\left(2x\right)\mathrm{cos}(x-\frac{\pi}{6})=\mathrm{sin}\left(2x\right)\mathrm{sin}(\frac{\pi}{6}-x)$

I gave a try using the$\mathrm{cos}(a-b)$ and $\mathrm{sin}(a-b)$ formulas, but it seems the problem complicated a little bit more.

I gave a try using the