Matte slightly smaller than picture I am framing

I bought a frame and matte for my picture that has a white border measuring 3/8". The matte is black, so I would like to see an even white border inside the black. The picture is just slightly bigger than the matte. I've been using scotch tape to get it in place. Each time I think I have it, when I get the frame altogether, one side or another shows a slight bit more picture edge (white) than the other and you can see on the other side it might just reach the matte.

Is there a trick to making everything line up? Would it help to buy white tape and place it all around the picture? Or does it just take 20+ times to get it right.