Find the value of the following: `tan^(-1)(tan((7pi)/6))`

Explanation

To find the value of \( \tan^{-1}(\tan(\frac{7\pi}{6})) \), we will follow these steps:

### Step 1: Understanding the Function
We know that the function \( \tan^{-1}(x) \) (or arctan) gives the angle whose tangent is \( x \). The output of \( \tan^{-1}(x) \) is restricted to the interval \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \).

### Step 2: Simplifying the Argument
We need to simplify \( \tan(\frac{7\pi}{6}) \). The angle \( \frac{7\pi}{6} \) can be rewritten in terms of a reference angle:
\[
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