2015 AMC 12B Problem 25

A bee starts flying from point P_0. She flies 1 inch due east to point P_1. For j \ge 1, once the bee reaches point P_j, she turns 30^{\circ} counterclockwise and then flies j+1 inches straight to point P_{j+1}. When the bee reaches P_{2015} she is exactly a \sqrt{b} + c \sqrt{d} inches away from P_0, where a, b, c and d are positive integers and b and d are not divisible by the square of any prime. What is a+b+c+d ?

\textbf{(A)}\; 2016 \qquad\textbf{(B)}\; 2024 \qquad\textbf{(C)}\; 2032 \qquad\textbf{(D)}\; 2040 \qquad\textbf{(E)}\; 2048

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.