(b) $1 – {\cos ^2}\theta – 2\cos \theta + \frac{1}{4} = 0$

$ \Rightarrow $ ${\cos ^2}\theta + 2\cos \theta – \frac{5}{4} = 0$

$ \Rightarrow $ $\cos \theta = \frac{{ – 2 \pm \sqrt {4 + 5} }}{2} = – 1 \pm \frac{3}{2}$

Since $|\cos \theta |\, \le 1$,

hence $\cos \theta = – 1 – \frac{3}{2}$ is ruled out.

$ \Rightarrow $ $\cos \theta = – 1 + \frac{3}{2} = \frac{1}{2} = \cos \left( {\frac{\pi }{3}} \right)$

$ \Rightarrow $ $\theta = 2n\pi \pm \frac{\pi }{3}$.