Tetrahedron's Insphere

A regular tetrahedron has edge length $6$. A sphere is tangent to all four faces of the tetrahedron (its insphere). Find the radius of the sphere. The answer is in the form $\frac{a\sqrt{b}}{c}$ for where $a$, $b$, $c$ are positive integers, $\gcd(a,c) = 1$, and $b$ is square-free. Input the answer as the sum $a+b+c$.