`tan(pi/4+theta)-tan(pi/4-theta)=2tan2theta`

Explanation

To prove the equation \( \tan\left(\frac{\pi}{4} + \theta\right) - \tan\left(\frac{\pi}{4} - \theta\right) = 2\tan(2\theta) \), we will start with the left-hand side and simplify it step by step.

### Step-by-Step Solution:

1. **Start with the Left-Hand Side:**
\[ LHS = \tan\left(\frac{\pi}{4} + \theta\right) - \tan\left(\frac{\pi}{4} - \theta\right) \]
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