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