Let $\theta$ be an angle such that $\tan \theta=\frac{3}{2}$ and $\csc \theta<0$. Find the exact values of $\sin \theta$ and $\cos \theta$.

Step 1 ：Let \(\theta\) be an angle such that \(\tan \theta=\frac{3}{2}\) and \(\csc \theta<0\). We are to find the exact values of \(\sin \theta\) and \(\cos \theta\).

Step 2 ：The tangent of an angle is positive in the first and third quadrants, while the cosecant of an angle is negative in the third and fourth quadrants. Therefore, the angle \(\theta\) must be in the third quadrant. In the third quadrant, both sine and cosine are negative.

Step 3 ：We know that \(\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{3}{2}\). We can use the Pythagorean identity \(\sin^2 \theta + \cos^2 \theta = 1\) to find the exact values of \(\sin \theta\) and \(\cos \theta\).

Step 4 ：By solving the Pythagorean identity, we find that the exact values of \(\sin \theta\) and \(\cos \theta\) are \(\boxed{-\frac{3}{\sqrt{13}}}\) and \(\boxed{-\frac{2}{\sqrt{13}}}\), respectively.