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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 $4x^3-3x-\cos\theta$.

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    Perhaps you could tell us the name of the textbook? (I guess it might be a typo.)2012-10-10
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    Did you look: http://en.wikipedia.org/wiki/Angle_trisection ?2012-10-10
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    If $\eta$ trisects $\theta$, i.e. $3\eta=\theta$, and $x=\cos\eta$, then $4x^2-3x-\cos\theta$ $=4\cos^3\eta-3\cos\eta-\cos\theta$ $=\cos(3\eta)-\cos\theta=0$. Is it possible that "$-$" should be where "$+$" appears in your question?2012-10-10

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