You are designing a diffraction grating that will disperse white light into its spectrum \((400-\mathrm{nm}\) violet to \(700-\mathrm{nm}\) red). In the first-order spectrum, you want the angular separation between the shortest and longest wavelengths to be \(12.0^{\circ}\).

(a) How many slits per millimeter should the grating have?

(b) How many complete full-color spectra will the grating produce, not counting the central bright fringe?