#Sintheta=-1/3#
We know that:
#Sin^2theta+cos^2theta=1#
#implies (-1/3)^2+cos^2theta=1#
#implies1/9+cos^2theta=1#
#implies cos^2theta=1-1/9=8/9#
#implies cos^2theta=8/9#
#implies costheta=+-sqrt(8/9)#
#implies costheta=+-sqrt8/3#
But Since the #theta# is in between #180^o and 270^o #. i.e The angle #theta# is in #3rd# quadrant.
Since #cos# is negative in #3rd# quadrant. Therefore, we take the negative value of #costheta#.
#implies costheta=-sqrt8/3#
Also we know that:
#Tantheta=Sintheta/costheta=(-1/3)/(-sqrt8/3)=1/sqrt8#
#implies Tantheta=1/sqrt8#
