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

Explanation

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

### Step 1: Start with the given equation
We are given:
\[ \tan \beta = \frac{\tan \alpha + \tan \gamma}{1 + \tan \alpha \tan \gamma} \]

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