Nghiệm của phương trình 2tanx + cotx = 2 sin2x + 1/sin2x là

A. $\left[\begin{array}{c}x=\frac{\mathrm{\pi }}{4}+k2\mathrm{\pi }\\ x=\pm \frac{\mathrm{\pi }}{6}+k\mathrm{\pi }\end{array}\right.\left(k\in Z\right)$

B. $\left[\begin{array}{c}x=\frac{\mathrm{\pi }}{4}+k\frac{\mathrm{\pi }}{2}\\ x=\pm \frac{\mathrm{\pi }}{6}+k\mathrm{\pi }\end{array}\right.\left(k\in Z\right)$

C. $\left[\begin{array}{c}x=\frac{\mathrm{\pi }}{4}+k\frac{\mathrm{\pi }}{2}\\ x=\frac{\mathrm{\pi }}{6}+k\mathrm{\pi }\end{array}\right.\left(k\in Z\right)$

D. $\left[\begin{array}{c}x=\frac{\mathrm{\pi }}{4}+k\frac{\mathrm{\pi }}{2}\\ x=-\frac{\mathrm{\pi }}{6}+k\mathrm{\pi }\end{array}\right.\left(k\in Z\right)$