1995 AIME Problem 12

Pyramid OABCD has square base ABCD, congruent edges \overline{OA}, \overline{OB}, \overline{OC}, and \overline{OD}, and \angle AOB=45^\circ. Let \theta be the measure of the dihedral angle formed by faces OAB and OBC. Given that \cos \theta=m+\sqrt{n}, where m_{} and n_{} are integers, find m+n.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.