Trigonometric Ratios of Multiple of an Angle

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. 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. Let $S$ be the set of all $\alpha \in R$ such that the equation, $\cos 2x+\alpha \sin x=2\alpha -7$ has a solution. Then $S$ is equal to:

1. $R$
2. $[2,6]$
3. $[1,4]$
4. $[3,7]$