question_answer

Let\[S=\left\{ x\in (-\pi ,\pi ):x\ne 0,\pm \frac{\pi }{2} \right\}\]. The sum of all distinct solutions for the equation \[\sqrt{3}\sec \,\,x+\cos ec\,\,x+2\,\,(\tan \,\,x-\cot \,\,x)=0\] in the set S is equal to

A)  \[-\frac{7\pi }{9}\]                    

B) \[-\frac{2\pi }{9}\]

C)  0        

D)  \[\frac{5\pi }{9}\]

E)  None of these