No. of solution of Trigo. equation.

[man111]

The Trigonometric equation is $sinx+3sin2x+sin3x = cosx+3cos2x+cos3x$ Where $x\in\left[0,2\pi\right]$.Then Calculate

$(i)$ No. of solution of $x$ in $\left[0,2\pi]$

$(ii)$ The Difference between the greatest and least value of $x$ is

$(iii)$ the Sum of The solution of $x$ in $\left[0,2\pi]$

[Полосин]

Transform $\sin x+\sin3x$ and $\cos x+\cos 3x$, then regroup the terms and factorize.