Find the value of expression: `sin(2tan^(-1)(1/3))+cos(tan^(-1)2sqrt(2))`

Explanation

To solve the expression \( \sin(2\tan^{-1}(1/3)) + \cos(\tan^{-1}(2\sqrt{2})) \), we will break it down into two parts and evaluate them step by step.

### Step 1: Evaluate \( \sin(2\tan^{-1}(1/3)) \)

Let \( \theta = \tan^{-1}(1/3) \). Then, we have:
\[ \tan(\theta) = \frac{1}{3} \]
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