2012 AIME I Problem 12

Let \triangle ABC be a right triangle with right angle at C. Let D and E be points on \overline{AB} with D between A and E such that \overline{CD} and \overline{CE} trisect \angle C. If \frac{DE}{BE} = \frac{8}{15}, then \tan B can be written as \frac{m \sqrt{p}}{n}, where m and n are relatively prime positive integers, and p is a positive integer not divisible by the square of any prime. Find m+n+p.

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.