Answer
$$-\frac{1}{\cot \left(t\right)}$$
Work Step by Step
Simplifying the expression using the Laws of Trigonometry, we find:
$$\frac{1}{2\csc \left(t\right)\cos \left(t\right)-3\cot \left(t\right)} \\ \frac{1}{2\cot \left(t\right)-3\cot \left(t\right)} \\ -\frac{1}{\cot \left(t\right)}$$