If \(\frac{1}{{{\rm{cosec\theta \;}} + {\rm{\;}}1}}{\rm{\;}} + {\rm{\;}}\frac{1}{{{\rm{cosec\theta }} - 1}}{\rm{\;}} = {\rm{\;}}2{\rm{sec\theta }},0^\circ < {\rm{\theta }} < 90^\circ ,\) then the value of \(\frac{{{\rm{tan\theta \;}} + {\rm{\;}}2\sec {\rm{\theta }}}}{{{\rm{cosec\theta }}}}\) is:

• A. \(\frac{{2{\rm{\;}} + {\rm{\;}}\sqrt 3 }}{2}\)
• B. \(\frac{{4{\rm{\;}} + {\rm{\;}}\sqrt 3 }}{2}\)
• C. \(\frac{{2{\rm{\;}} + {\rm{\;}}\sqrt 2 }}{2}\)
• D. \(\frac{{4{\rm{\;}} + {\rm{\;}}\sqrt 2 }}{2}\)