I was given the above problem for homework. There is (what seems to be) a relevant proof in my textbook regarding the impossibility of trisecting $\pi/3$. In this proof, the identity
$$\cos 3\theta = 4\cos^3 \theta -3\cos\theta$$
is used. Rearranging, we get $ 0 = 4\cos^3 \theta-3\cos\theta-\cos 3\theta$. I know if the given equation were $4x^3-3x-\cos\theta$, my homework problem would be relatively easy. At this point, however, I'm not sure where to go. A push in the right direction would be very appreciated.
Edit: The question isn't actually out of the textbook (Galois Theory by Stewart). It's on a worksheet my teacher typed up, which makes me think it might be a typo as well. In fact, the textbook asks the analogous question for $4x^3-3x-\cos\theta$.