The first two terms of a sequence are a_{1}=1 and a_{2}=\dfrac{1}{\sqrt{3}}. For n \geq 1,
a_{n+2}=\dfrac{a_{n}+a_{n+1}}{1-a_{n} a_{n+1}} \text {. }
What is \left|a_{2009}\right| ?
Answer Choices
A. 0
B. 2-\sqrt{3}
C. \dfrac{1}{\sqrt{3}}
D. 1
E. 2+\sqrt{3}