$4\cos\dfrac{x}{3}.\cos\dfrac{\pi+x}{3}\cos\dfrac{\pi-x}{3}$
$=4\cos\dfrac{x}{3}.\dfrac{1}{2}\Big( \cos\dfrac{2\pi}{3}+\cos\dfrac{2x}{3}\Big)$
$=2\cos\dfrac{x}{3}\cos\dfrac{2x}{3}+2\cos\dfrac{x}{3}.\cos\dfrac{2\pi}{3}$
$=\cos x+\cos\dfrac{-x}{3}-\cos\dfrac{x}{3}$
$=\cos x$