solve for $A$ in $\cos A+\cos2A+\cos3A=0$ Solve for $A$ where, $0°\leq A\leq 360°$
$\cos A+\cos2A+\cos3A=0$
My attempt;
Here, 
$$\cos A+\cos2A+\cos3A=0$$
$$\cos A+2\cos^2A-1+4\cos^3A-3\cos A=0$$
$$4\cos^3A+2\cos^2A-2\cos A-1=0$$.
Now, what should I do to move on?

$$4cos^{ 3 }A+2cos^{ 2 }A-2cosA-1=0\\ 2\cos ^{ 2 }{ A } \left( 2\cos { A } +1 \right) -\left( 2\cos { A } +1 \right) =0\\ \left( 2\cos { A } +1 \right) \left( 2\cos ^{ 2 }{ A } -1 \right) =0\\ \cos { A } =-\frac { 1 }{ 2 } ,\cos ^{ 2 }{ A } =\frac { 1 }{ 2 } \Rightarrow \cos { A } =\pm \frac { \sqrt { 2 }  }{ 2 } \\ $$ can you proceed?
