Let $\theta$ be an angle such that $\cos \theta=\frac{2}{3}$ and $\cot \theta< 0$. Find the exact values of $\tan \theta$ and $\csc \theta$.
\[
\begin{array}{l}
\tan \theta= \\
\csc \theta=
\end{array}
\]

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

Step 2 ：The cosine of an angle is positive in both the first and fourth quadrants, but cotangent is negative in the second and fourth quadrants. Therefore, the angle must be in the fourth quadrant. In the fourth quadrant, cosine is positive, sine is negative, and tangent (which is sine divided by cosine) is also negative.

Step 3 ：The sine of the angle can be found using the Pythagorean identity \(\sin^2\theta + \cos^2\theta = 1\).

Step 4 ：Once we have the sine, we can find the tangent and cosecant. The tangent of an angle is the sine divided by the cosine, and the cosecant is the reciprocal of the sine.

Step 5 ：Using the given value of cosine, we find that \(\cos \theta = 0.6666666666666666\).

Step 6 ：Using the Pythagorean identity, we find that \(\sin \theta = -0.7453559924999299\).

Step 7 ：Then, we find that \(\tan \theta = -1.118033988749895\) and \(\csc \theta = -1.3416407864998738\).

Step 8 ：The exact values of \(\tan \theta\) and \(\csc \theta\) are \(\boxed{-1.118033988749895}\) and \(\boxed{-1.3416407864998738}\) respectively.