`cos(3x+pi/6) + cosx=0`

`<=> cos ( 3x + pi/6 ) = - cos x `

`<=> cos ( 3x + pi/6 ) =  cos(pi- x) `

`<=>` $\left[\begin{matrix} 3x+\dfrac{\pi}{6}=\pi-x+k2\pi\\3x+\dfrac{\pi}{6}=-\pi+x+k2\pi\end{matrix}\right.$

`<=>` $\left[\begin{matrix} 4x=\dfrac{5\pi}{6}+k2\pi\\2x=-\dfrac{7\pi}{6}+k2\pi\end{matrix}\right.$

`<=>` $\left[\begin{matrix} x=\dfrac{5\pi}{24}+\dfrac{k\pi}{2}\\x=-\dfrac{7\pi}{12}+k\pi\end{matrix}\right.$ `( k in ZZ)`