Explanation

Use the co-function identity cot 2θ = tan(90° − 2θ). Then tan 6θ = tan(90° − 2θ), and within the given range the arguments must be equal: 6θ = 90° − 2θ. Solving gives 8θ = 90°, so θ = 11.25°. Therefore 4θ = 45°, and sec 45° = 1/cos 45° = √2. The condition 0 < 6θ < π/2 guarantees we take the principal branch of the equality. Hence option (A) √2.