Let tan alpha, tan beta and tan gamma, a...

Let `tan alpha, tan beta and tan gamma, alpha, beta, gamma ne ((2n-1)pi)/(2), n in N` be the slopes of three line segments OA, OB and OC, respectively, where O is origin. If circumcentre of `DeltaABC` coincides with origin and its orthocontre lies on y-axis, then the value of `((cos 3alpha+cos 3beta +cos 3 gamma)/(cos alpha cos beta cos gamma))^(2)` is equal to _________.

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