A diffraction grating is designed to have the$$n$-$order maximum at angular position$$$,$ measured from the central maximum, for light with a wavelength of$$$.$

Given that$$n$=3,$$=11\mathrm{.}8$ degrees, and$$$=556$ nm$,$ what is the ruling constant $($number of lines per length$)$ of the grating?

Enter your answer in units of lines$-$per$-$micrometer.$$ For example, if your calculations produce a value of$1\mathrm{.}2310^5$lines$/$m$,$ first convert units to$1\mathrm{.}2310^5$lines$/(10^6$m$)$ or $0\mathrm{.}123$ lines$/$m$,$ then enter your answer as $0\mathrm{.}123.$