Can they really be distinct?

Algebra Level 4

Let \(a\), \(b\), and \(c\) be distinct complex numbers such that

\[\frac { a }{ 1-b } =\frac { b }{ 1-c } =\frac { c }{ 1-a } = k\]

where \(k\) is a complex number.

Find the sum of all values of \(k\).

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