2009 AMC 12A Problem 25

The first two terms of a sequence are a_1 = 1 and a_2 = \frac {1}{\sqrt3}. For n\ge1,

a_{n + 2} = \frac {a_n + a_{n + 1}}{1 - a_na_{n + 1}}.

What is |a_{2009}|?

\textbf{(A)}\ 0\qquad \textbf{(B)}\ 2 - \sqrt3\qquad \textbf{(C)}\ \frac {1}{\sqrt3}\qquad \textbf{(D)}\ 1\qquad \textbf{(E)}\ 2 + \sqrt3

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