If $y=f(x)$ is the solution of the differential equation $\left(1+\cos ^2 x\right) f^{\prime}(x)-4 \sin 2 x-f(x) \sin 2 x=0$ when $f(0)=0$, then $f\left(\frac{\pi}{3}\right)=$

• A

  $3$
• Correct answer
  B

  $\frac{12}{5}$
• C

  $\frac{3}{5}$
• D

  $4$

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