If 2 cos 2A = √3 and A is acute, find : (i) A (ii) sin 3A (iii) sin2 (75° - A) + cos2 (45° + A)

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If 4 sin² θ - 1 = 0 and angle θ is less than 90°, find the value of θ and hence the value of cos² θ + tan² θ.