First, solve over 0≤𝜃<2𝜋. Then, write an expression for ALL the solutions.
A different way to word this question:
Let 𝑟𝜃=2cos𝜃−1sin𝜃+1. Find all zeros of 𝑟 in the interval 0≤𝜃<2𝜋. Then, find all zeros in the domain of 𝑟.