Not Another Triangle Solving Problem!

Geometry Level 5

\(\triangle ABC\) satisfies the following properties:

1) \(cosB+cosC=1\)

2) \(\angle C-\angle B=46^\circ\)

Let \(O,I,H\) denote the circumcenter, incenter, orthocenter of \(\triangle ABC\) respectively. Find \(\angle OIH\) in degrees.

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