If 3 tanθ = \(2\sqrt 3 \) sinθ, 0° < θ < 90°, then the value of \(\rm \frac{{\cos e{c^2}2\,\theta + {{\cot }^2}2\,\theta }}{{{{\sin }^2}\,\theta + {{\tan }^2}2\,\theta }}\) is:
1
\(\frac{{20}}{{39}}\)
2
\(\frac{{20}}{{27}}\)
3
\(\frac{{4}}{{13}}\)
4
\(\frac{{4}}{{3}}\)