If $\sin (\pi \cos x) = \cos (\pi \sin x),$ enter all possible values of $\sin 2x,$ separated by commas.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
If $\sin (\pi \cos x) = \cos (\pi \sin x),$ enter all possible values of $\sin 2x,$ separated by commas.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{3}{4}, -\frac{3}{4}
If $\sin (\pi \cos x) = \cos (\pi \sin x),$ enter all possible values of $\sin 2x,$ separated by commas.
train