Let the transformation \( y(x) = e^x \nu(x) \) reduce the ordinary differential equation \( x \frac{d^2y}{dx^2} + 2(1 - x) \frac{dy}{dx} + (x - 2) y = 0 \), where \( \alpha, \beta, \gamma \) are real constants. Then, the arithmetic mean of \( \alpha, \beta, \gamma \) is \(\underline{\hspace{2cm}}\) (round off to three decimal places).