\noindent\(\displaystyle \cos\frac{x}{3}=\frac{1}{2 (\cos x+\sqrt{-1+\cos^2 x})^{1/3}}+\frac{1}{2} (\cos x+\sqrt{-1+\cos^2 x})^{1/3}\\
\cos\frac{x}{3}=-\frac{1+i \sqrt{3}}{4 (\cos x+\sqrt{-1+\cos^2 x})^{1/3}}-\frac{1}{4} (1-i \sqrt{3}) (\cos x+\sqrt{-1+\cos^2 x})^{1/3}\\
\cos\frac{x}{3}=-\frac{1-i \sqrt{3}}{4 (\cos x+\sqrt{-1+\cos^2 x})^{1/3}}-\frac{1}{4} (1+i \sqrt{3}) (\cos x+\sqrt{-1+\cos^2 x})^{1/3}\)