Question

Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)
csc θ(2 cos θ − 1) = 0

Answer 1

$-1\le\sin\theta\le1\implies(\csc\theta\le-1)\cup(\csc\theta\ge1)$

which means $\csc\theta=0$ has no solution, and we can omit that factor.

This leaves us with

$2\cos\theta-1=0\implies\cos\theta=\dfrac12$

which occurs for $\theta=\pm\dfrac\pi3+2n\pi$.