$\left.\begin{array}{cc}{\left[\begin{array}{l}\text { Law of Cosines } \\ {[\text { Similar triangles (other) }}\end{array}\right]}\end{array}\right]$

In triangle $ABC$, $AC=2\sqrt{3}$, $AB=\sqrt{7}$, $BC=1$. Outside the triangle, a point $K$ is taken such that segment $KC$ intersects segment $AB$ at a point different from $B$, and the triangle with vertices $K, A$, and $C$ is similar to the original triangle. Find the angle $AKC$, given that angle $KAC$ is obtuse.