In triangle $ABC,$ $\angle A,$ $\angle B,$ and $\angle C$ form an arithmetic sequence.  The length of the altitude from $B$ to $\overline{AC}$ is equal to $AB - BC.$  Find all possible values of
\[\sin \frac{C - A}{2}.\]Enter all possible values, separated by commas.
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In triangle $ABC,$ $\angle A,$ $\angle B,$ and $\angle C$ form an arithmetic sequence.  The length of the altitude from $B$ to $\overline{AC}$ is equal to $AB - BC.$  Find all possible values of
\[\sin \frac{C - A}{2}.\]Enter all possible values, separated by commas.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
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user
\frac{1}{2}
In triangle $ABC,$ $\angle A,$ $\angle B,$ and $\angle C$ form an arithmetic sequence.  The length of the altitude from $B$ to $\overline{AC}$ is equal to $AB - BC.$  Find all possible values of
\[\sin \frac{C - A}{2}.\]Enter all possible values, separated by commas.
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