Obviously, one cannot calculate two independent lattice parameters using just one experimental value. After you get more data, you can proceed using the equation
In fact, there are not two but three parameters since you have also to take into consideration the zero-shift to compute the cell parameters. You need more Bragg peaks !
The ratio c / a = (8/3) ^ 0.5 is true for an ideal HCP structure. It corresponds to the space group P63 / mmc. Here, wurtzite crystallises in the P63mc and thus does not satisfy to c / a = (8/3) ^ 0.5