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maybe this is just not that interesting, but it is bugging me

I don't get what you mean. \(\cos(\frac{\pi}{5})\) is not a root for \(4x^2−2x−1\).

Oh but it is. One does not lightly challenge the Great Satellite.

Oh right.

so there must be some connection here.

**correction, -1 = z^5 = ....

i meant of course i replaced all the sines by cosines

oh i see my mistake.

and now i see why, he gets to divide by sine because it is set equal zero, not -1.