Factor out the $cos\left(x\right)$ from the equation.

$\cos(x)(2\sin(x)+1)\ =\ 0$

Use the Zero Product Property to solve for $x$.

$\text{cos}(x)\ =\ 0 \ \text{or 2sin}(x) + 1\ =\ 0$

Find all the solutions to these statements either using a unit circle or by graphing the functions on a graphing calculator. Do not just take this inverse on your calculator, it will only give you one possible solution. Remember, each of the $4$ solutions repeats every $2πn$ radians.