Find all values of Ɵ in the interval [0 degrees, 360 degrees) that satisfy the equation?

Question

9 sin^2 Ɵ + 12 sin + 4 = 0

round to the nearest tenth

Answer 1

9 sin^2 Ɵ + 12 sin Ɵ + 4 = 0
This quadratic equation has single solution:
sin Ɵ = -2/3
Corresponding angles are
Ɵ = arcsin(-2/3)

Ɵ = 221.8 degrees
and
Ɵ = 318.2 degrees

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Answer 2

(3 sin θ + 2)(3 sin θ + 2) = 0
sin θ = - 2 / 3
θ = 221.8° , 318.2°