If `("tan"(theta+alpha))/a=""("tan"(theta+beta))/b=""("tan"(theta+gamma))/c` `(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 solve the given problem step by step, we start with the equation provided:

Given:
\[ \frac{\tan(\theta + \alpha)}{a} = \frac{\tan(\theta + \beta)}{b} = \frac{\tan(\theta + \gamma)}{c} \]

Let’s denote the common value as \( k \):
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