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How do I solve for $x$ in $$x\left(x^3+\sin(x)\cos(x)\right)-\big(\sin(x)\big)^2=0$$

I hate when I find something that looks simple, that I should know how to do, but it holds me up.

I could come up with an approximate answer using Taylor's, but how do I solve this?

(btw, WolframAlpha tells me the answer, but I want to know how it's solved.)

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    Maybe some wise inequality does a good job here.2012-08-22

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