Two extremely narrow, parallel slits are cut in a sheet of cardboard, with the width \(a\) of each slit very much smaller than the distance \(d\) between them. When the slits are illuminated by a coherent beam of \(620-\mathrm{nm}\) light, the angular position of the two third-order bright fringes is \(\pm 4. 27^{\circ}\). The cardboard between the slits is then cut out so that the sheet contains only a single opening. When this opening is illuminated by the \(620-\mathrm{nm}\) light, what are the angular positions of the \(n=1,2,3\) dark fringes?