Evaluate: `tan{1/2cos^(-1)(sqrt5/3)}`

Explanation

To evaluate \( \tan\left(\frac{1}{2} \cos^{-1}\left(\frac{\sqrt{5}}{3}\right)\right) \), we can follow these steps:

### Step 1: Set up the equation
Let \( \theta = \frac{1}{2} \cos^{-1}\left(\frac{\sqrt{5}}{3}\right) \). Therefore, we have:
\[ \cos(2\theta) = \frac{\sqrt{5}}{3} \]

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