Three-year olds are sticklers for "FAIR" and instantly call "THAT'S NOT FAIR" on things they don't feel benefit them. You mentioned you took your li'l guy out of his routine...was he prepared for this in any way before hand? "We may have to go to grandma's instead of to Suzy's party if grandma doesn't feel better tomorrow. If that happens, we'll invite Suzy over to give her her present then and plan a special day with her." In the morning "grandma still feels sick, so we'll go over and see what we can do to make her feel better. We'll leave right after your morning snack. Can you help choose some quiet toys to bring?" Sort of run up to it. Acknowledge whatever the problem is, validate the feelings if expressed "I know you're sad about missing the party, but we'll see Suzy soon"
Now, that only works if it's foreseeable. If it's a question of nap time needing to be too early, or lunch being too late, or nap being too late, you'll have other issues, because the child is conditioned to nap/eat at a certain time, and a change (being expected to eat/nap before he's hungry) can produce rebellion, and we all know that delaying things till he's exhausted and cranky and hungry is a recipe for disaster in and of itself.
Children that age see a break in a comfortable established routine as a threat. They are becoming more and more socially aware by that age, and are starting to feel awkward if they don't know what to expect. They generally feel safe and secure in their routines, and a change without warning or explanation can be devastatingly confusing, prompting a meltdown. The best prevention is an explanation "After school today, we'll be doing something different. After I pick you up from pre-school, we'll have a special snack and then we'll go do some clothes shopping for you. We'll go to this store, and you can tell mommy what colour clothes you'd like to look for, and we'll try to find some we both like. Then mommy will help you try them on, and we'll look in the mirror to see if they look good on you. Then we'll buy the clothes we like, and come home and you can snuggle up and we'll read a book, and then show daddy your new clothes when he gets home"
Pre-schoolers who then throw a tantrum AFTER that can be calmly hugged, and then you step back and make eye contact and say "I can see you're very upset about something, but I can't understand why you're upset because you're crying so hard. When you stop crying and use your words, I'll listen to why you're upset, and we'll try to fix the problem." Then once the child gets calmer, ask if he'd like a nice cool washcloth to make his face feel better, give him one if he wants, then LISTEN. Be prepared to rub his back and say "Easy, keep using your words" if he starts to cry again. LISTEN to his problem...it may be easily mitigated by something. I've watched a three year old have hysterics because he'd wanted cucumber with his lunch and instead got carrot sticks (which he also loved, but wanted cucumber). Instant, zero-to-sixty tantrum. You'd have thought he was being murdered. Once he calmed down enough to tell me what was wrong, I told him of course he could have cucumber, and that he didn't need to have a tantrum, he could have just asked. Three minutes later, he was munching happily and somewhat understood that if he uses words, sometimes things will be better, but no one can understand the tantrum, and if they don't understand, they can't make it better.
All THAT said...sometimes long, uncharacteristic tantrums are a sign that he's coming down with a cold or something, or is over-tired, or something happened at school that was threatening to him (bullying, for instance) and he was looking forward to the safety and security of home and routines...and they changed.
If it's constant, talk to your paediatrician. Look at other factors as well...loss of sleep, needing extra sleep, appetite changes, etc.
And, above all, big hugs..that can be so hard to have a screamer!