Is there any proof of the criterion of determining maximal ideal in a commutative ring with unity by Third Isomorphism Theorem?

Question

Theorem. Let $R$ be a commutative ring with unity $1$ and $M$ is an ideal of $R$. Show that $M$ is maximal iff $\dfrac{R}{M}$ is a field.

In the proof of this theorem the methods so far I have seen are some variant of Theorem 3.4.2 of this or an argument similar to that sketched here in the proof of Theorem 18.8.

My question is,

Is there any proof of the above theorem using the Third Isomorphism Theorem?