Answer
$$\emptyset $$
Work Step by Step
$$\eqalign{
& 2{\cos ^2}\theta + 2\cos \theta + 1 = 0 \cr
& {\text{Let }}x = \cos \theta \cr
& 2{x^2} + 2x + 1 = 0 \cr
& {\text{Solve by using the quadratic formula}} \cr
& x = \frac{{2 \pm \sqrt {{{\left( 2 \right)}^2} - 4\left( 2 \right)\left( 1 \right)} }}{{2\left( 2 \right)}} \cr
& x = \frac{{2 \pm \sqrt { - 4} }}{2} \cr
& x = 1 \pm i \cr
& {\text{The equation has no real solutions, then}} \cr
& {\text{No solution}} \cr
& \emptyset \cr} $$
