If `theta_(2) and theta_(2)` are the angles made by the lines `(x^(2)+y^(2))(cos^(2) theta sin^(2) alpha+ sin^(2) theta)= (x tan alpha- y sin theta)^(2)` with positive axis of x in the anticlock wise direction, if `theta=(pi)/(6), tan theta_(1)+ tan theta_(2)`, equals

Options

A. `(-(8)/(3)) sin^(2) alpha`
B. `(-8sqrt(3))"cosec" 2 alpha`
C. `(-(8)/(3))"cosec" 2 alpha`
D. `(-4 sqrt(3))"cosec" 2 alpha`

Answer

C