Of Course Vieta's formula, but...

Algebra Level 5

f(x)=x32x2+6x1=0f(x)=x^3-2x^2+6x-1=0

The three roots of the above equation are α,β,γ\alpha,\beta,\gamma, then what is

αα2α+1+ββ2β+1+γγ2γ+1=?\frac{\alpha}{\alpha^2-\alpha+1}+\frac{\beta}{\beta^2-\beta+1}+\frac{\gamma}{\gamma^2-\gamma+1}=?

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