A value of \({\rm{\theta }} \in \left( {0,{\rm{\;}}\frac{{\rm{\pi }}}{3}} \right),{\rm{\;for\;which}}\left| {\begin{array}{*{20}{c}}{1 + {\rm{co}}{{\rm{s}}^2}{\rm{\theta }}}&{{\rm{si}}{{\rm{n}}^2}{\rm{\theta }}}&{4{\rm{\;cos\;}}6{\rm{\theta }}}\\{{\rm{co}}{{\rm{s}}^2}{\rm{\theta }}}&{1 + {\rm{si}}{{\rm{n}}^2}{\rm{\theta }}}&{4{\rm{\;cos\;}}6{\rm{\theta }}}\\{{\rm{co}}{{\rm{s}}^2}{\rm{\theta }}}&{{\rm{si}}{{\rm{n}}^2}{\rm{\theta }}}&{1 + 4{\rm{\;cos\;}}6{\rm{\theta }}}\end{array}} \right| = 0\), is:

• A. \(\frac{\pi }{9}\)
• B. \(\frac{\pi }{{18}}\)
• C. \(\frac{{7\pi }}{{24}}\)
• D. \(\frac{{7\pi }}{{36}}\)