In $\mathrm{△}\mathrm{ABC}\text{, if }{\mathrm{c}}^4-2\left({\mathrm{a}}^2+{\mathrm{b}}^2\right){\mathrm{c}}^2+{\mathrm{a}}^4+{\mathrm{a}}^2{\mathrm{b}}^2+{\mathrm{b}}^4=0\text{ then ∠}\mathrm{C}=$

$$\begin{gathered} {\left({\mathrm{c}}^2\right)}^2+{\left({\mathrm{a}}^2\right)}^2+{\left({\mathrm{b}}^2\right)}^2-2{\mathrm{a}}^2{\mathrm{c}}^2-2{\mathrm{b}}^2{\mathrm{c}}^2+2{\mathrm{a}}^2{\mathrm{b}}^2={\mathrm{a}}^2{\mathrm{b}}^2 \\ \Rightarrow {\left({\mathrm{a}}^2+{\mathrm{b}}^2-{\mathrm{c}}^2\right)}^2={\mathrm{a}}^2{\mathrm{b}}^2 \\ \Rightarrow {\mathrm{a}}^2+{\mathrm{b}}^2-{\mathrm{c}}^2=\pm \mathrm{ab} \\ \Rightarrow \frac{{\mathrm{a}}^2+{\mathrm{b}}^2-{\mathrm{c}}^2}{2\mathrm{ab}}=\pm \frac{1}{2}\Rightarrow \mathrm{cosC}=\pm \frac{1}{2} \\ \therefore \mathrm{C}=60° \mathrm{or} 120° \end{gathered}$$