Let \( P(x) \) be a polynomial given by \( P(x) = (1 + ix)^4 \cdot (1 - ix)^4 \). Using the binomial theorem and properties of complex numbers, find the coefficient of \( x^2 \) in the expanded form of \( P(x) \). Let's think step by step and output the final answer within \boxed{}.
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