For $n$ a positive integer, define $f_1(n) = n$. Then for $i$ a positive integer, define $f_{i+1}(n) = f_i(n)^{f_i(n)}$. Determine $f_{100}(75) \pmod{17}$. Justify your answer.

Let's think step by step and output the final answer within \boxed{}.
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