Trigonometric Ratios of Multiple of an Angle

Q. The number of common solution(s) of the trigonometric equations $\cos 2x+(1-\sqrt{3})=(2-\sqrt{3})\cos x$ and $\sin 3x=2\sin x,$ satisfying the inequality $\sqrt{3}\tan x-1\ge 0$ in $[0,5\pi ]$ is

Q. For $x\in (0,\pi ),$ the equation $\sin x+2\sin 2x-\sin 3x=3$ has

1. no solution
2. one solution
3. two solutions
4. three solutions

Q. If the sum of the solutions of the equation $\cos (\frac{\pi }{3}-\theta )\cos (\frac{\pi }{3}+\theta )-\frac{\sec \theta }{4}=0$ in $[0,10\pi ]$ is $k\pi ,$ then the value of $k$ is