Question 1029571
Okay, from
2 sin θ + 1 = csc θ
2 sin θ + 1 = 1/sin θ
Multiply by sin θ and get
2 sin^2 θ + sin θ = 1
2 sin^2 θ + sin θ - 1 = 0
Now factor and solve
(2 sin θ - 1)(sin θ + 1) = 0
so that
sin θ = 1/2  and θ = 30 and 150 degrees
AND
sin θ = -1 and θ = 270 degrees