If 3 tan θ = \(2\sqrt 3 \) sin θ, 0° < θ < 90°, then the value of \(\frac{3}{4}\left( {\frac{{{\rm{cose}}{{\rm{c}}^2}\,2{\rm{\theta }}\,{\rm{ + }}\,{\rm{co}}{{\rm{t}}^2}2{\rm{\theta }}}}{{{\rm{si}}{{\rm{n}}^2}\,{\rm{\theta }}\,{\rm{ + }}\,{\rm{ta}}{{\rm{n}}^2}2{\rm{\theta }}}}} \right)\) is:
1
\(\frac{5}{{13}}\)
2
\(\frac{3}{{13}}\)
3
\(\frac{7}{{13}}\)
4
\(\frac{1}{{13}}\)