Answer
For $\theta$ near $\pi / 3$ ,
$$
f(\theta) \approx \cos \frac{\pi}{3}-\left(\sin \frac{\pi}{3}\right)\left(\theta-\frac{\pi}{3}\right)
$$
For $\theta$ near 2$\pi / 3$ ,
$$
f(\theta) \approx \cos \frac{2 \pi}{3}-\left(\sin \frac{2 \pi}{3}\right)\left(\theta-\frac{2 \pi}{3}\right)
$$
Work Step by Step
For $\theta$ near $\pi / 3$ ,
$$
f(\theta) \approx \cos \frac{\pi}{3}-\left(\sin \frac{\pi}{3}\right)\left(\theta-\frac{\pi}{3}\right)
$$
For $\theta$ near 2$\pi / 3$ ,
$$
f(\theta) \approx \cos \frac{2 \pi}{3}-\left(\sin \frac{2 \pi}{3}\right)\left(\theta-\frac{2 \pi}{3}\right)
$$
