1996 AIME Problem 15

In parallelogram ABCD, let O be the intersection of diagonals \overline{AC} and \overline{BD}. Angles CAB and DBC are each twice as large as angle DBA, and angle ACB is r times as large as angle AOB. Find the greatest integer that does not exceed 1000r.

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.