Digital Root of 3 Consecutive Numbers ending in Multiple of 3

Theorem
Let $n$, $n + 1$ and $n + 2$ be positive integers such that $n + 2$ is a multiple of $3$.

Let $m = n + \left({n + 1}\right) + \left({n + 2}\right)$.

Then the digital root of $m$ is $6$.

Proof
Let $n + 2$ be expressed as $3 r$ for some positive integer $r$.

Then:

The result follows from Digital Root of Number equals its Excess over Multiple of 9.