If `("tan"(theta+alpha))/a=""("tan"(theta+beta))/b=""("tan"(theta+gamma))/c` then prove `(a+b)/(a-b)sin^2(alpha-beta)+(b+c)/(b-c)sin^2(beta-gamma)+(c+a)/(c-a)sin^2(gamma-alpha)=0`

Explanation

To prove the equation

\[ \frac{(a+b)}{(a-b)} \sin^2(\alpha - \beta) + \frac{(b+c)}{(b-c)} \sin^2(\beta - \gamma) + \frac{(c+a)}{(c-a)} \sin^2(\gamma - \alpha) = 0, \]

given that

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