Use the Sharon Schamber's glue trick.
When you come to the end, fold the end piece onto your quilt at a 45 degree angle and press.
Put a small line of glue along the fold at the 45 degree edge.
Now lay your beginning piece of binding on top of the glue and press with an iron. This will make it stick.
Carefully, holding the glued part, unfold the rest of the binding tails.
The fold line will be visible as to where to sew, and the ends will be held together with the glue.
It always works.