I know this sounds goofy, but I recently discovered that my kids LOVE frozen veggies. Not cooked frozen, but frozen. I was pouring the veggies into a dish to cook one night and some fell on the floor and my kids were quickly fighting over them, to eat them frozen. So, now I serve them that way at a lot of the meals. Hey, if it works, right? :) They go for the french cut green beans, the carrot/pea mix or the mixed veggies that have corn/peas/carrots/lima beans etc. I haven't tried broccoli or cauliflower that way becuase they are so big, but my kids will usually eat those raw or cooked, most days they prefer them uncooked.
Also, my mom brought over a can of carrots, I never buy canned veggies but she brought some and they all love the canned carrots, so I keep some on hand for the days when they refuse all other things.
Other tips...cut them different, like julianne strips of carrot or zucchini, shred them rather than slice, cut the carrots like a flower, make it a game between he and daddy "Daddy, can you see if you can eat your veggies before Connor does?" That one works with getting them to drink their milk at our house!
What about offering them at different times of the day, rather than meals? Maybe they have become a power struggle at meal time that might go unnoticed if presented at snack time or in a different location than the table: carrots while reading a book on the floor?
Oh, another thing that worked this summer with my daycare boy, make up weird names for them. Instead of baby carrots, they became ostrich toes, broccoli became oak trees. Use whatever he is into: dinosaurs etc.
I read someplace too that you can give them toothpicks and let them build with the veggies, like make a robot (3 years old should be ok with supervision to use the toothpicks) then they "get to" eat whatever they built. Mix in some veggies, like use some grapes, some cherry tomatoes, slightly softened carrots(microwave in a bit of water, the toothpicks go in easier) etc.
So, try to make it not about eating veggies, but about finding a way to make it fun so he doesn't realize he is eating veggies. You can also shred/dice/puree them and sneak them in if all else fails. I used to do that to get veggies in the kids I was a nanny for. I would put finely shredded carrots etc into meatloaf, pureed onion, bell peppers, carrots, zucchini into spagetti sauce.
Good luck! This too shall pass!
M.