Coordinate Geometry: JEE Main 2021 Mathematics question

Let tan$\alpha$, tan$\beta$ and tan$\gamma$; $\alpha$, $\beta$, $\gamma$ $\ne$ ${{(2n - 1)\pi } \over 2}$, n$\in$N be the slopes of three line segments OA, OB and OC, respectively, where O is origin. If circumcentre of $\Delta$ABC coincides with origin and its orthocentre lies on y-axis, then the value of ${\left( {{{\cos 3\alpha + \cos 3\beta + \cos 3\gamma } \over {\cos \alpha \cos \beta \cos \gamma }}} \right)^2}$ is equal to ____________.