Answer
$$x=\frac{\pi }{3}+2\pi n,\:x=\pi +2\pi n$$
Work Step by Step
We solve the equation using the properties of trigonometric functions. Note, there is a general solution since trigonometric identities go up and down and this can pass through a given value of y many times. Solving this, we find:
$$\left(\cos \left(x\right)+1\right)^2-3\sin ^2\left(x\right)=0 \\ \left(1+\cos \left(x\right)\right)^2-\left(1-\cos ^2\left(x\right)\right)\cdot \:3=0 \\ \cos \left(x\right)=\frac{1}{2},\:\cos \left(x\right)=-1 \\ x=\frac{\pi }{3}+2\pi n,\:x=\pi +2\pi n$$
