Floor Function

Determine the absolute value of the sum $$\lfloor 2013\sin{0^\circ} \rfloor + \lfloor 2013\sin{1^\circ} \rfloor + \cdots + \lfloor 2013\sin{359^\circ} \rfloor,$$ where $\lfloor x \rfloor$ denotes the greatest integer less than or equal to $x$.

(You may use the fact that $\sin{n^\circ}$ is irrational for positive integers $n$ not divisible by $30$.)

Source: 2012-2013 Winter Online Math Open