Let \triangle P Q R be a triangle with \angle P=75^{\circ} and \angle Q=60^{\circ}. A regular hexagon A B C D E F with side length 1 is drawn inside \triangle P Q R so that side \overline{A B} lies on \overline{P Q}, side \overline{C D} lies on \overline{Q R}, and one of the remaining vertices lies on \overline{R P}. There are positive integers a, b, c, and d such that the area of \triangle P Q R 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.