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The circumcentre of a triangle with vert...

The circumcentre of a triangle with vertices `(a, a tan alpha), B(b, b tan beta)` and `C (c, c tan gamma)` lies at the origin, where `0 lt alpha beta, gamma lt pi//2` and `a+ beta+gamma = pi`. Show that its orthocentre lies on the line `4 cos((alpha)/(2))cos((beta)/(2))cos((gamma)/(2))x - 4 sin ((alpha)/(2))sin((beta)/(2))sin((gamma)/(2))y=y`

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