Solve the following math problem step by step. The last line of your response should be of the form Answer: \boxed{$Answer} where $Answer is the answer to the problem.

<image>In $\odot O, \overline{E C}$ and $\overline{A B}$ are diameters, and $\angle B O D \cong \angle D O E \cong \angle E O F \cong \angle F O A$
Find $m\widehat{B C}$