Chapter 7 - Analytic Trigonometry - 7.3 Trigonometric Equations - 7.3 Assess Your Understanding - Page 467: 67

$\pi$

Step 1. Rewrite the equation $1-cos^2\theta=6cos\theta+6 \longrightarrow cos^2\theta+6cos\theta+5=0 \longrightarrow (cos\theta+1)(cos\theta+5)=0$. Thus $cos\theta=-1$ or $cos\theta=-5$ Step 2. For $cos\theta=-1$, we have $\theta=\pi$ Step 3. For $cos\theta=-5$, we have $\theta=none$