$f \left( \frac 1{2001} \right) + f \left( \frac 2{2001} \right) + f \left( \frac 3{2001} \right) +\cdots + f \left( \frac {2000}{2001} \right)$

Let $f(x) = \dfrac 2{4^x+2}$ for real numbers $x$. Evaluate the expression above.

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