If an angle (θ) is divided in two parts such that the Tangent of one part is (m) times the Tangent of the other, then prove that their ...?

If an angle (θ)  is divided in two parts such that the Tangent of one part is (m) times the Tangent of the other, then prove that their difference (ϕ)  is obtained from the equation 

sin ϕ = sin θ [ (m-1)/(m+1) ]

31/55 

Update:

Michael : Hi. Appreciable approach . Very nice.

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