If `tanbeta=(tanalpha+tangamma)/(1+tanalphatangamma)dot` prove that `sin2beta=(sin2alpha+sin2gamma)/(1+sin2alphasin2gamma)` .

Explanation

To prove that \( \sin 2\beta = \frac{\sin 2\alpha + \sin 2\gamma}{1 + \sin 2\alpha \sin 2\gamma} \) given that \( \tan \beta = \frac{\tan \alpha + \tan \gamma}{1 + \tan \alpha \tan \gamma} \), we can follow these steps:

### Step 1: Express \( \tan \beta \) in terms of sine and cosine
We know that:
\[ \tan \beta = \frac{\sin \beta}{\cos \beta} \]
From the given equation, we can express \( \tan \beta \) as:
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