Find the principal value of: `tan^(-1)(-1)`

Explanation

To find the principal value of \( \tan^{-1}(-1) \), we can follow these steps:

### Step 1: Understand the Function
The function \( \tan^{-1}(x) \) or \( \arctan(x) \) gives the angle whose tangent is \( x \). The principal value of \( \tan^{-1}(x) \) is defined in the range \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \).

### Step 2: Set Up the Equation
We need to find \( \theta \) such that:
\[
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