Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the line x+2 √ 2 y=4. If the co-ordinates of the vertex A are…

Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the line $\displaystyle x+2 \sqrt{2} y=4$. If the co-ordinates of the vertex $\displaystyle A$ are $\displaystyle (\alpha, \beta)$, then the greatest integer less than or equal to $\displaystyle |\alpha+\sqrt{2} \beta|$ is