If √2 tan2θ = √6 and 0° < θ

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√2 tan2θ = √6

⇒ tan2θ =	√6	= √3
	√2

⇒ tan2θ = tan 60°
⇒ 2θ = 60° ⇒ θ = 30°
∴ sinθ + √3 cosθ – 2 tan2θ
= sin 30° + √3 cos 30° – 2 tan²30°

=	1	+ √3 ×	√3	– 2		1		²
	2		2			√3

=	1	+	3	−	2
	2		2		3

=	3 + 9 − 4	=	8	=	4
	6		6		3