If cotθ + tanθ = 2secθ, 0°< θ < 90°, then the value of \(\frac{{{\rm{tan}}2{\rm{\theta }} - {\rm{sec\theta }}}}{{{\rm{cot}}2{\rm{\theta \;}} + {\rm{\;cosec\theta }}}}\) is:

• A. \(\frac{{2\sqrt 3 - 1}}{{11}}\)
• B. \(\frac{{3 - \sqrt 2 }}{{11}}\)
• C. \(\frac{{2\sqrt 3 - 2}}{{11}}\)
• D. \(\frac{{3 - \sqrt 2 }}{5}\)