Answer
$$\frac{2\tan \left(1-\frac{1}{z}\right)}{3}$$
Work Step by Step
Simplifying the expression using trigonometric identities, we find:
$$\frac{2\sin \left(1-\frac{1}{z}\right)}{3\cos \left(1-\frac{1}{z}\right)} \\ \frac{2\tan \left(1-\frac{1}{z}\right)}{3}$$