4 Positive Integers in Arithmetic Sequence which have Same Euler Phi Value

Theorem
The following sets of $4$ positive integers which form an arithmetic sequence are the smallest which all have the same Euler $\phi$ value:
 * $72, 78, 84, 90$
 * $216, 222, 228, 234$
 * $76 \, 236, 76 \, 242, 76 \, 248, 76 \, 254$

Proof
demonstrating that this is indeed an arithmetic sequence, with a common difference of $6$.

Now we show:

demonstrating that this is indeed an arithmetic sequence, with a common difference of $6$.

Now we show: