Chapter 7 - Section 7.4 - Basic Trigonometric Equations - 7.4 Exercises - Page 569: 47

there is no real solution

$\cos ^{2}\theta -\cos \theta -6=0\Rightarrow $ $\cos \theta =\dfrac {1\pm \sqrt {1+4\times 6}}{2}=\dfrac {1\pm 5}{2}=3;-2$ $cos\theta $ is in (-1,1) interval so it can not be greater than 1 or smaller than $-1$ so there is no real solution