b) Solve $3 \cos 2 \theta+\cos \theta=-1 \quad\left(0^{\circ} \leq \theta \leq 360^{\circ}\right)$

Step 1 ：Given the trigonometric equation \(3 \cos 2 \theta+\cos \theta=-1 \) where \(0^{\circ} \leq \theta \leq 360^{\circ}\)

Step 2 ：We can solve it by using the double angle formula for cosine, which is \(\cos 2\theta = 1 - 2\sin^2\theta\). We substitute this into the equation and then solve for \(\sin\theta\)

Step 3 ：The solutions are in radians. We need to convert them to degrees and only consider the solutions in the range \(0^{\circ} \leq \theta \leq 360^{\circ}\)

Step 4 ：The solutions to the equation in degrees are approximately 60.0000000000000 and 131.810314895779

Step 5 ：Final Answer: The solutions to the equation \(3 \cos 2 \theta+\cos \theta=-1 \quad\left(0^{\circ} \leq \theta \leq 360^{\circ}\right)\) are \(\boxed{60^{\circ}}\) and \(\boxed{131.81^{\circ}}\)