A.C.
Most kids need at least one nap until they are 4 yrs old. Usually that nap is 2-3 hours long. If he's getting less sleep and not being able to sleep at night, he might be lacking sleep rather than needing less. It's harder to fall asleep if he's been up too long during the day. Sleep begets more sleep! I'm not sure when you put him down for that nap. Try putting him down a half hour earlier to see if he'll sleep longer. Then put him down earlier at night. Kids tend to wake up the same time even if you put them down earlier. And they wake up earlier when you put them down later. Also, teething can interrupt naps and sleep at night. Molars tend to be more painful.
Good luck and I hope he gets more rest.