Let f(x)=3 x^{3}-5 x^{2}+2 x-6. If the roots of f are given by \alpha, \beta, and \gamma, find
\left(\frac{1}{\alpha-2}\right)^{2}+\left(\frac{1}{\beta-2}\right)^{2}+\left(\frac{1}{\gamma-2}\right)^{2}.
Let f(x)=3 x^{3}-5 x^{2}+2 x-6. If the roots of f are given by \alpha, \beta, and \gamma, find
\left(\frac{1}{\alpha-2}\right)^{2}+\left(\frac{1}{\beta-2}\right)^{2}+\left(\frac{1}{\gamma-2}\right)^{2}.