2018 AMC 12B Problem 16

The solutions to the equation (z+6)^8=81 are connected in the complex plane to form a convex regular polygon, three of whose vertices are labeled A,B, and C. What is the least possible area of \triangle ABC?

\textbf{(A) } \frac{1}{6}\sqrt{6} \qquad \textbf{(B) } \frac{3}{2}\sqrt{2}-\frac{3}{2} \qquad \textbf{(C) } 2\sqrt3-3\sqrt2 \qquad \textbf{(D) } \frac{1}{2}\sqrt{2} \qquad \textbf{(E) } \sqrt 3-1

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.