Of Course Vieta's formula, but...

Algebra Level 5

\[f(x)=x^3-2x^2+6x-1=0\]

The three roots of the above equation are \(\alpha,\beta,\gamma\), then what is

\[\frac{\alpha}{\alpha^2-\alpha+1}+\frac{\beta}{\beta^2-\beta+1}+\frac{\gamma}{\gamma^2-\gamma+1}=?\]

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