Let \(P=\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\…

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

[JEE Main 2023, 8 Apr (Shift 1)]