<s>[INST] Solve the equation: $\cos^2(x)+\cos^2(2x)+\cos^2(3x)=1$ How to solve the equation 

$$\cos^2(x)+\cos^2(2x)+\cos^2(3x)=1$$

Can anyone give me some hints?
 [/INST] $\cos^2(x)+[2 \cos^2x-1]^2 +[4 \cos^3 x-3 \cos x]^2 = 1$, Simplify the equation to get: $ \cos^2 x [8 \cos^4 x - 10 \cos^2 x + 3] = 0$. Hope this will help.
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