Algenometry

Algebra Level 5

\[\displaystyle\prod\limits_{i= 1}^{2015} {{{\left( {1 + {a_i}^2} \right)}}} + \displaystyle\prod\limits_{i = 1}^{2015} {{{\left( {1 - {a_i}^2} \right)}}} \]

If \(0 \le a_1, a_2, ..., a_{2015} \le 1\), and the maximum value of the above expression is \(A\), find \(\ln A \).

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