If $\alpha$ and $\beta$ are the solutions of $\cot x=-\sqrt{3}$ in $\left[\mathrm{0,2}\pi \right]$ and $\alpha$ and $\gamma$ are the solutions of $\mathrm{cosec}x=-2$ in $\left[\mathrm{0,2}\pi \right],$ then the value of $\frac{\left|\alpha -\beta \right|}{\beta +\gamma }$ is equal to

• Correct answer
  A

  $\frac{1}{2}$
• B

  $2$
• C

  $\frac{1}{3}$
• D

  $3$

Hence, the correct answer is option: 'A'.