Recall this identity:
#1+cot^2(θ)=csc^2(θ)#
#csc^2(θ)=11/9" "# (assuming that the radical only comprises the #11#).
#1+cot^2(θ)=11/9#
#cot^2(θ)=11/9 - 9/9 = 2/9#
#cot(θ)=+-sqrt(2/9)=+- sqrt(2)/3#
We're between #π/2# and #π# (the second quadrant). Here, cosine is negative and sine is positive; thus, cotangent (cosine over sine) is negative. The negative answer is what we're looking for.
#cot(θ)=-sqrt(2)/3#