Let tan α, tan β and tan γ; α, β, γ ≠ ((2 n -1) π)/2, n ∈ N be the slopes of three line segments OA, OB and OC, respectively, where O is origin. If…

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