#tan^2x+4tanx+2=0# can be solved using binomial formula
#tanx=(-4+-sqrt(4^2-4*1*2))/2=(-4+-sqrt8)/2=-2+-sqrt2#
i.e. either #tanx=-2+sqrt2=-2+1.4142=-0.5858#
i.e. #x=-0.53# and in #[0,2pi}# #x=3.1416-0.53=2.6117# or #x=2.6117+3.1416=5.7533#
and if #x=-2-sqrt2=-3.4142#, #x=-1.2859# ans in #[0,2pi)#
#x=3.1416-1.2859=1.8557# or #x=3.1416+1.8557=4.9973#