If $\alpha ,\beta ,\gamma$ are the real roots of the equation $x^3-3a{x}^2+3bx-1=0$ then the centroid of the triangle whose vertices are the points  $\left({\alpha }_1\frac{1}{\alpha }\right)$ ,$\left(\beta ,\frac{1}{\beta }\right)$ and $\left(\gamma ,\frac{1}{\gamma }\right)$ is the point