Prove the following identities, where the angles involved are acute angles for which the trigonometric ratios are defined:

(sin A + sec A)² + (cos A + cosec A)² = (1 + sec A cosec A)².

If 7 sin² θ + 3 cos² θ = 4, 0° ≤ θ ≤ 90°, then find the value of θ.