Step 5Fasten base, back, and the divider
iImage Information

Use beads of carpentar's glue at the joining surface. Start fastening the drywall screws to secure the two pieces together. Reinforce the base with the back using three right angle brackets for extra strength. The brackets I used, came with small size screws. Attach the divider piece with the glue to the back and base piece. Fasten it with drwall screws from each side. Wipe out the access glue with a paper towel. Note that the divider in the picture below is for the bottom shelf of my design. The divider is put on the left side of the shelf. For the top shelf, move the divider to the right hand side.
if you want a feeling of extra security you could cut your end pieces so that the grain runs diagonally (from the top back to the front bottom corner, not from the top front to the back bottom.) make them the same size as the divider (will require a larger board to cut them from, or let the leading corner be cut off, won't hurt the strength, just a different look) and screw them from below and behind as you did with the divider. this way will both give you stronger glue joints than gluing onto end grain and somewhat hide the screw heads on the back and bottom. this is probably the strongest connection you can make without some sort of proper joinery involving fancy cutting.
however, if you are really attached to metal reinforcement, you could counter sink the brackets with a chisel or router (too fiddly) or put the brackets on the outside so they go behind and under (lumpy but the book are safe) or get the kind that are flat L shapes (much stronger than the kind you are using now, not that it is needed) and hide them between the end caps and the shelf/back, screwing through them as you put the end pieces on (still a bit lumpy if you don't want to cut notches for them, but it might be possible to hide the gaps with caulk or wood putty before painting.)