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