Prove that: `tanA + tan(60^(@)+A) + tan(120^(@)+A)=3tan3A`

Explanation

To prove the identity \( \tan A + \tan(60^\circ + A) + \tan(120^\circ + A) = 3 \tan 3A \), we will follow these steps:

### Step 1: Use the tangent addition formula
We start with the left-hand side (LHS) of the equation:
\[ LHS = \tan A + \tan(60^\circ + A) + \tan(120^\circ + A) \]
Using the tangent addition formula, \( \tan(x + y) = \frac{\tan x + \tan y}{1 - \tan x \tan y} \), we can express \( \tan(60^\circ + A) \) and \( \tan(120^\circ + A) \).
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