<image>Given: In parallelogram ABCD, point O is the intersection of diagonals AC and BD, ∠EOB = 30°, and EF is a segment with point O as its midpoint.
(1) When EF rotates around point O arbitrarily (EF does not coincide with BD), is quadrilateral BFDE a parallelogram? If so, please provide proof; if not, please provide a reason;
(2) By how many degrees must EF rotate around point O for quadrilateral BFDE to become a rhombus?