2 sin2 θ = 3 − 5 cos θ

2sin2θ = 3 − 5cosθ  ......      add 5cosθ to both sides

2sin2θ + 5cosθ = 3             the easiest way to solve this is by graphing..... (I'm using x instead of theta)

Here's the graph.......https://www.desmos.com/calculator/wi0mp1onme

This is an odd looking one!!!....the solutions are at 70° and 335°  on [0, 360]