Solve for C. \[ \mathrm{C}=[? \] Law of Cosines: $c^{2}=a^{2}+b^{2}-2 a b \cdot \cos C$ Measure of Angle C Enter

Step 1 ：The question is asking to solve for C in the context of the Law of Cosines. The Law of Cosines is typically used to find an unknown side or angle in a triangle when you know the lengths of the other two sides and one of their included angles. However, in this case, we are given the formula but no specific values for a, b, or c, and we are asked to solve for C. This means we need to rearrange the formula to solve for C.

Step 2 ：Rearrange the Law of Cosines to solve for C: \(c^{2}=a^{2}+b^{2}-2 a b \cdot \cos C\)

Step 3 ：The solutions for C in the Law of Cosines are \(C = -\cos^{-1}\left(\frac{a^{2} + b^{2} - c^{2}}{2ab}\right) + 2\pi\) and \(C = \cos^{-1}\left(\frac{a^{2} + b^{2} - c^{2}}{2ab}\right)\)

Step 4 ：Final Answer: \(\boxed{C = -\cos^{-1}\left(\frac{a^{2} + b^{2} - c^{2}}{2ab}\right) + 2\pi, C = \cos^{-1}\left(\frac{a^{2} + b^{2} - c^{2}}{2ab}\right)}\)