2013 AIME I Problem 12

Let \bigtriangleup PQR be a triangle with \angle P = 75^o and \angle Q = 60^o. A regular hexagon ABCDEF with side length 1 is drawn inside \triangle PQR so that side \overline{AB} lies on \overline{PQ}, side \overline{CD} lies on \overline{QR}, and one of the remaining vertices lies on \overline{RP}. There are positive integers a, b, c, and d such that the area of \triangle PQR can be expressed in the form \frac{a+b\sqrt{c}}{d}, where a and d are relatively prime, and c is not divisible by the square of any prime. Find a+b+c+d.

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.