If 3 tan^ 2 θ – 4√3tan θ + 3 =0 then find the acute angle θ.

If 3 tan ² θ – 4√3tan θ + 3 =0 then find the acute angle θ.

Solution
3 tan 2 θ – 4√3tan θ + 3 =0  [Given]
∴ 3 tan2 θ – 3√3 tanθ  -  √3 tanθ  + 3 = 0
∴ 3tanθ (tanθ - √3) – √3 (tanθ - √3 ) = 0
∴ (tanθ - √3) (3tanθ - √3) = 0
∴ tanθ - √3 = 0	OR	3tanθ - √3  = 0
∴ tan θ  = √3	OR	3 tan θ = √3
	OR	tanθ = √3 3
	OR	tanθ = 1 √3
But, tan 600 = √3		Also, tan 300 = 1 √3
∴ θ = 600	OR	θ = 300
Ans. ∴ the value of θ is either 300 OR 600