As a child care provider I found this to be quite common in both the two's classroom and the threes classroom so the information that it "usually ends around two" is not accurate in the reality of my experience.
What I would suggest is two fold:
Your child does need reassurances from you in your words and behavior. Are you having a hard time with the separation too? Your child can pick up on this if you are. He or she does need reassurances from you in your words and behavior. This may sound harsh, but the upset - fit throwing kids that maintained this behavior for longer periods tended to be kids whose parents did one of two things: slip away, or respond pleadingly or with bribes (who often seemed really upset themselves).
Resist the temptation to "slip away". I don't know your situation, but if you've "snuck out" or slipped away while the child was distracted, it made it easier for you and momentarily easier for the child care provider, but not for your child. It is a form of dishonesty and does not reassure your child of trusting in your return even when you do return day after day, after day, after day.
Avoiding pleading and begging for your child to calm down. This is attention that is negative but it is delaying your leaving. Therefore it is working for your child.
Instead, develop a "leaving routine". Put stuff in the cubby, snuggle your child for a couple of minutes while you go over the schedule (never rush this, but don't let it take longer than 5-10 minutes either). What is going on at the daycare that he/she can be excited about today? What is for lunch? and finally, when will you return so he or she has an activity "marker" for when to expect you. Something like, "You'll _ (fill in the blank with something super fun for your kid), have lunch, take your nap and then after you've played a little more I'll be here and I'm looking forward to seeing you then and hearing about your day". With Alice we then finished up with a "nuzzle" (resting our foreheads together), a "monster kiss" (rubbing of noses), a hug and then a regular kiss. Peal them off you, pass them over to their teacher/childcare provider, blow a kiss and walk away with a happy confident demeanor. A good care provider will then distract your child with something fun and after a few weeks your child will begin to trust in the routine.