AMC 12 2010b Problem 13

In $\triangle ABC$, $\cos(2A-B)+\sin(A+B)=2$ and $AB=4$. What is $BC$?

\textbf{(A)}\ \sqrt{2} \textbf{(B)}\ \sqrt{3} \textbf{(C)}\ 2 \textbf{(D)}\ 2\sqrt{2} \textbf{(E)}\ 2\sqrt{3}