find all values of 2sin theta-3csc theta=-5
2sinØ - 3cscØ = -5
2sinØ - 3/sinØ = -5
multiply each term by sinØ
2 sin^2 Ø - 3 = -5sinØ
2 sin^2 Ø + 5sinØ - 3 = 0
(2sinØ - 1)(sinØ + 3 ) = 0
sinØ = 1/2 or sinØ = -3 , the last is not possible
if sinØ = 1/2
then Ø = 30° or Ø = 150°
or
Ø = π/6 or 5π/6