Solving $\cos^2 x+\cos^2 2x +\cos^2 3x=1$ I picked this up from the IMO 1962.

Solve for $x$: 
  $$\cos^2 x+\cos^2 2x +\cos^2 3x=1$$ 

At first I thought it was trivial to bring this in an IMO, but I realized approaching it directly brings a power of 6 which is not all too friendly.
Is there a sneaky way to solve this?

Use double angles to get the equivalent equation 
$$\cos(0x) + \cos(2x) + \cos(4x) + \cos(6x) = 0.$$
Pair (first and last term) and (middle ones) to get the equivalent form
$$\cos(x)\cos(2x)\cos(3x) = 0.$$
