Let P= [(√ 3)/2, 1/2; -1/2, (√ 3)/2], A= [1, 1; 0, 1] and Q=P A P^T. If P^T Q^2007 P= [a, b; c, d], then 2 a+b-3 c-4 d equal to

Let $\displaystyle P=\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right], A=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]$ and $\displaystyle Q=P A P^T$. If $\displaystyle P^T Q^{2007} P=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$, then $\displaystyle 2 a+b-3 c-4 d$ equal to