For the following two (02) items:
Let $\cos (2x+3y)=\frac{1}{2}$ and $\cos (3x+2y)=\frac{\sqrt{3}}{2}$  where  $-\pi <(2x+3y)<\pi $ and $-\pi <(3x+2y)<\pi .$

How many values does (x + y) have?

For the following two (02) items:
Let $\cos (2x+3y)=\frac{1}{2}$ and $\cos (3x+2y)=\frac{\sqrt{3}}{2}$  where  $-\pi <(2x+3y)<\pi $ and $-\pi <(3x+2y)<\pi .$

How many values does (y-x) have?

How many values of $\theta $, where$- \pi < \theta < \pi$ satisfy both the equations $\cot \theta =-\sqrt{3}$ and $\csc \theta =-2$ simultaneously?

If $x+\frac{1}{x}=2\cos \theta$ then what is $x^{3}+\frac{1}{x^{3}}$ equal to?