The total number of solutions of |cot⁡x|=cot⁡x+1sin⁡x, x∈[0,3π] is equal to

|cot⁡x|    =cot⁡x+1sin⁡x If  cot⁡x>0⇒ cot⁡x=cot⁡x+1sin⁡x=0⇒ 1sin⁡x=0,which is not possibleIf cot⁡x≤0⇒ −cot⁡x=cot⁡x+1sin⁡x⇒ −2cot⁡x=1sin⁡x or  cos⁡x=−12⇒ x=2π3,8π3