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 $$m+n.$$

(第十三届AIME1995 第12题)