Question

$$Sin2x+ \sqrt{ 3 } \times Cos2x+1 \geq 0$$

Solve for x

$x\in \begin{bmatrix}\pi n_{1}+\frac{3\pi }{4},\pi n_{1}+\frac{17\pi }{12}\end{bmatrix}\text{, }n_{1}\in \mathrm{Z}$