Let \(a, b, c, d\) be distinct complex numbers such that
\(|a| = |b| = |c| = |d| = 1\) and \(a + b + c + d = 0.\)
Find the maximum value of
\(|(a + b)(a + c)(a + d)(b + c)(b + d)(c + d)|\).
I know I asked this question before, but there was no response so I thought I would try again. I honestly do not know the answer, anyone with complex number experience, help would be greatly appreciated.