When the epoxy has set you can remove the tape. After it has fully cured (again, 24 hours) then you can sand down any rough parts with sandpaper. You ...
It was your favorite chair until SNAP! a piece was broken. You might be getting ready to dump it or put it in front of your house as a lost cause for someone else to adopt, but wait! It can likely be fixed and you can have many years of satisfied sitting ahead of you.
All right, let's fix it!
Step 1: Clean the wound
Remove the splinters at the ends of each piece. You want the two pieces to easily go back together and even have a slight gap between them for the epoxy to fill.