If θ is positive acute angle and 7cos2θ + 3sin2θ = 4, then value of θ is?

Answer: Option A

$$\begin{array}{rl}& \text{7co}{\text{s}}^2\theta +3{\sin }^2\theta =4\\ & 7\text{co}{\text{s}}^2\theta +3\left(1-\text{co}{\text{s}}^2\theta \right)-4=0\\ & 7\text{co}{\text{s}}^2\theta -3\text{co}{\text{s}}^2\theta +3-4=0\\ & 4\text{co}{\text{s}}^2\theta =1\\ & \text{co}{\text{s}}^2\theta =\frac{1}{4}\\ & \text{cos}\theta =\frac{1}{2}\\ & \cos \theta =\text{cos}60^{\circ }\\ & \theta =60^{\circ }\end{array}$$