When your current approach isn't getting results is the best possible time to try something else, because you'll be able to see quickly whether it works. Sounds like your little guy is doing what 3yo's typically do. And there are positive things you can do to address it.
ALL behavior, in adult or child, is a strategy to meet some need. If he's not listening or responding to your requirements, it's because at three he has a completely natural need for more control in his little world. This is not for the purpose of "testing limits" or "pushing boundaries" or "challenging your authority," as many moms believe, but a completely natural stage in his development, as he learns how things work, both physically and emotionally.
It's important to keep our adult expectations in line with what is realistic for a young child, or else everything will feel like a battle. Your son's growing need for autonomy and control is a good thing, if you have a master plan that takes those very real needs into account. ALL little kids need opportunities to make choices, to manipulate the world, to play, to relax, to internalize all they are learning.
Unfortunately, little kids have very little life experience, so they do what they know. That often looks like simple stubbornness and resistance to their parents, especially if the child is overextended, over-scheduled, overtired or hungry. If you'd like to apply some of the latest and best parenting research to see how effective it can be, there's a most wonderful little book I use with my grandson and other small people, called How to Talk So Kids Will Listen, and Listen So Kids Will Talk, by Faber and Mazlish. Another terrific resource for slightly younger kids is Dr. Harvey Karp's approach in The Happiest Toddler on the Block. (You can google his name or the book title to see several videos demonstrating one of his techniques.)
I hope you'll give it a try; it just may save your sanity. It teaches you surefire techniques for getting on your son's wavelength, thus drawing him onto yours. It shows brilliant ways to nurture his own problem-solving skills. This results in more cheerfully cooperative behavior, and less stressful days for both of you.