Continued fractions or continued fun?

Algebra Level 4

\[\large \cfrac{1}{3 + \cfrac{1}{2 + \cfrac{1}{1 + \cfrac{1}{3 + \cfrac{1}{2 + \cfrac{1}{1 + \cfrac{1}{\ddots }}}}}}}\]

Evaluate the infinitely nested function above. Give your answer to 3 decimal places.

Clarification: The \(3,2,1,3,2,1,3,2,1,\ldots \) pattern in repeating.

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