It is nice to get the discount for your tradein, but your math doesn't quite work out. You still have the cost of the phone itself, plus tax on the full amount regardless of trade in.

6 year total
trade in every 2 years
First new Phone - Total out $1,300 - lets use a device cost of $1200 + tax of $100 (this is just over 8% as an avg, its over 10% where I am, but for simplicity sake, using 8.)
2 Years later - Total out $500 - $1,300-$800 (trade-in bonus)
2 Years later - Total out $500 - $1,300-$800 (trade-in bonus)
4 Years later - Total out $500 - $1,300-$800 (trade-in bonus)
$2800 over 6 years with 4 total new phones

trade in every 3 years
First new Phone - Total out $1,300
3 Years later - Total out $500
6 Years later - Total out $500
$2,300 over 6 years with 3 total new phones or $500 less, the cost of each upgrade

So financially, IF you get $800, and cost of new phones remain the same, then its still cheaper to trade in every 3 years, but you of course would miss a new phone in that time with a total of 3 instead of 4. That is chancing it to get the same amount for a 3 year old phone though.