Answer
Positive.
Work Step by Step
$90^{\circ}\lt\theta\lt 180^{\circ}\implies45^{\circ}\lt\frac{\theta}{2}\lt 90^{\circ}$
The cotangent function is positive as the angle $\frac{\theta}{2}$ is in between $45^{\circ}$ and $90^{\circ}$( This interval is in the first quadrant and cotangent function is positive in the first quadrant ).
