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Given, 3cos 2 θ = 2 + sin 2 θ
3cos 2 θ - sin 2  θ = 2
3cos 2 θ - (1 - cos 2  θ) = 2
4cos 2 θ = 3
cos 2 θ = (3/4)
cosθ = √3/2 (Since, in options maximum value of 'θ' is 90 o  therefore, we will take the positive root only)
cosθ = cos30 o
θ = 30 o
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