There exists a positive real number $x$ such that $ \cos (\arctan (x)) = x $. Find the value of $x^2$.
Question:
There exists a positive real number $x$ such that $ \cos (\arctan (x)) = x $. Find the value of $x^2$.
Answer:
Let's think step by step.

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\frac{-1 + \sqrt{5}}{2}
There exists a positive real number $x$ such that $ \cos (\arctan (x)) = x $. Find the value of $x^2$.
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