Geometry Problem 426: Triangle, Circumradius, Circumcenter, Concurrent Cevians

The figure shows a triangle ABC with
circumcenter O and circumradius R. The cevians AD, BE, and CF are
concurrent at O. Prove that \(\dfrac{2}{R}=\dfrac{1}{AD}+\dfrac{1}{BE}+\dfrac{1}{CF}\) .