Triangle ODB is isosceles, with COB = pi/2, therefore OBC = pi/4. Line OA bisects angle COB, so angle AOB = pi/8. OBAC is a rhombus so diagonals cut at pi/2, using angle sum of a triangle you get angle OBC = 3pi/8.
OBC = OBD + DBC,
DBC = 3pi/8 - pi/4 = pi/8
This may not be the best method...