Find the equations of the tangent plane and normal line to surface $z = \sin(2x - y)$ at point $P(\frac{-\pi}{3}, \frac{\pi}{2}, -\frac{1}{2})$

Question

Here is what I have so far :

$$ z - z_0 = F_x(x_0,y_0)(X - x_0) + F_y(x_0,y_0)(Y - y_0) \\P: z - (-\frac{1}{2}) = \cos(\frac{-7\pi}{6})(X - (-\frac{\pi}{3})) -\cos(\frac{-7\pi}{6})(y- \frac{\pi}{2}) \\ L: t(-\frac{\pi}{3}, \frac{\pi}{2}, -\frac{1}{2}) $$