Factoring the LHS:

`6 sin^2θ − 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` (that is, `pi/6` or `(5pi)/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:

Graph of trigonometric equation solution

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

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