Just the sides given, can you find the angle?

Geometry Level 4

In \(\triangle ABC, \) if

\[a^4 + b^4 + c^4 = 2c^2\big(a^2 +b^2\big), \]

then the possible measure(s) of \(\angle C\) could be \(\text{__________}.\)

\(\)
Details and Assumptions:

\(a,b,c\) are the sides of \(\triangle ABC\) opposite to \(\angle A , \angle B, \angle C\) respectively.
\(\angle C\) is measured in radians.

\[ \frac \pi6\] \[ \frac \pi6, \frac {5\pi }6\] \[ \frac \pi4 \] \[ \frac \pi4, \frac {3\pi }4 \] \[ \frac \pi4, \frac {5\pi }6\] \[ \frac \pi4, \frac \pi 6, \frac \pi 3 \] \[ \frac \pi3, \frac {2\pi }3\] \[ \frac \pi3, \frac {3\pi }4\]

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