Prove: `tan^(-1)(2/3)=1/2tan^(-1)(12/5)`

Explanation

To prove that \( \tan^{-1}\left(\frac{2}{3}\right) = \frac{1}{2} \tan^{-1}\left(\frac{12}{5}\right) \), we will start by manipulating the left-hand side (LHS) and show that it equals the right-hand side (RHS).

### Step 1: Set LHS
Let:
\[ y = \tan^{-1}\left(\frac{2}{3}\right) \]
Then, we can express this as:
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