Factoring the LHS:

6 sin² θ − sin θ − 1 = 0

(2 sin θ − 1)(3 sin θ + 1) = 0

So either

2 sin θ − 1 = 0

sin θ = 1/2

θ will be in 1st and 2nd quadrants.

θ = 0.52360, 2.6180 (ie π/6, 5π/6)

OR

3 sin θ + 1 = 0

sin θ = − 1/3

θ will be in 3rd and 4th quadrants.

θ = 3. 4814, 5. 9433

Checking our solution on a graph:

So θ = 0.52360, 2.6180, 3. 4814, 5. 9433