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

Explanation

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

### Step 1: Understand the function
The function \( \cos^{-1}(x) \) is the inverse cosine function, which gives us the angle whose cosine is \( x \). The principal value of \( \cos^{-1}(x) \) is defined in the range \( [0, \pi] \).

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