Let $a$ and $b$ be nonzero complex numbers such that
\[|a| = |b| = |a + b|.\]Find the sum of all possible values of $\frac{a}{b}.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $a$ and $b$ be nonzero complex numbers such that
\[|a| = |b| = |a + b|.\]Find the sum of all possible values of $\frac{a}{b}.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
-1
Let $a$ and $b$ be nonzero complex numbers such that
\[|a| = |b| = |a + b|.\]Find the sum of all possible values of $\frac{a}{b}.$
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