\[\LARGE { i }^{ { i }^{ i^{.^{.^{.}}} } } \]

For \( i = \sqrt{-1} \), the value of the infinitely nested exponent above is equal to \(A + Bi \) for real values \(A\) and \(B\).

Find the value of \({ A }^{ 2 }+{ B }^{ 2 }\) to 3 decimal places.

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