Find the value of `tan^(-1)(tan(3pi)/4)`

Explanation

To find the value of \(\tan^{-1}(\tan(3\pi/4))\), we need to use the properties of the inverse trigonometric functions and the periodicity of the tangent function. Here is the step-by-step solution:

1. **Identify the range of the inverse tangent function:**
The range of \(\tan^{-1}(x)\) is \((- \frac{\pi}{2}, \frac{\pi}{2})\).

2. **Express the given angle in terms of a principal angle:**
The given angle is \(\frac{3\pi}{4}\). We need to express this angle in the range \((- \frac{\pi}{2}, \frac{\pi}{2})\).

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