question_answer

If \[{{x}_{1}},\] \[{{x}_{2}},\] \[{{x}_{3}},\] \[{{x}_{4}}\] are roots of the equation \[{{x}^{4}}-{{x}^{3}}\sin 2\beta +{{x}^{2}}\cos 2\beta -x\,\,\cos \beta -\sin \beta =0,\] then \[{{\tan }^{-1}}{{x}_{1}}+{{\tan }^{-1}}{{x}_{2}}+{{\tan }^{-1}}{{x}_{3}}+{{\tan }^{-1}}{{x}_{4}}=\]

A) \[\beta \]                                   

B)  \[\frac{\pi }{0}-\beta \]

C)  \[\pi -\beta \]                 

D)  \[-\beta \]

E)  None of these