In triangle $ABC,$
\[a^4 + b^4 + c^4 = 2c^2 (a^2 + b^2).\]Enter the possible values of $\angle C,$ in degrees, separated by commas.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
In triangle $ABC,$
\[a^4 + b^4 + c^4 = 2c^2 (a^2 + b^2).\]Enter the possible values of $\angle C,$ in degrees, separated by commas.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
45^\circ, 135^\circ
In triangle $ABC,$
\[a^4 + b^4 + c^4 = 2c^2 (a^2 + b^2).\]Enter the possible values of $\angle C,$ in degrees, separated by commas.
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