If 3 tan² θ - 1 = 0, find cos 2θ, given that θ is acute.

If sec θ = cosec θ and 0° ≤ θ ≤ 90°, find the value of θ.

If 4 cos² x° - 1 = 0 and 0 ≤ x ≤ 90, find

(i) x

(ii) sin² x° + cos² x°

(iii) cos² x° - sin² x°.

If sin 3x = 1 and 0° ≤ 3x ≤ 90°, find the values of

(i) sin x

(ii) cos 2x

(iii) tan² x - sec² x.