Find the principal value of `sec^(-1)(sqrt2)`.

Explanation

To find the principal value of \( \sec^{-1}(\sqrt{2}) \), we can follow these steps:

### Step 1: Understand the definition of the inverse secant function
The function \( \sec^{-1}(x) \) is defined for \( x \) such that \( |x| \geq 1 \). The range of \( \sec^{-1}(x) \) is \( [0, \frac{\pi}{2}) \cup (\frac{\pi}{2}, \pi] \).

### Step 2: Set up the equation
Let \( \theta = \sec^{-1}(\sqrt{2}) \). By the definition of the inverse secant function, we have:
\[
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