Solution:

Given,

7 sin² θ + 3 cos² θ = 4, 0° ≤ θ ≤ 90°

3 sin² θ + 3 cos² θ + 4 sin² θ = 4

3 (sin² θ + 3 cos² θ) + 4 sin² θ = 4

3 (1) + 4 sin² θ = 4

4 sin² θ = 4 – 3

sin² θ = ¼

Taking square-root on both sides, we get

sin θ = ½

Thus, θ = 30^o