Can you attack this function?

Algebra Level 4

If f(x)=4x4x+2f(x)=\frac{4^x}{4^x+2}, where xQx€Q, then f(12007)+f(22007)+...+f(20062007)f(\frac{1}{2007})+f(\frac{2}{2007})+...+f(\frac{2006}{2007}) equals to ??

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