Where 0<=x<360, Solve the equation

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Where 0<=x<360, Solve the equation

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\[3\sin x-5+\csc x=0\]
\[3\sin ^2x-5\sin x+1=0\]
But I simplified that to \[\sin ^{2}x-3\sin x+1\]

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Other answers:

I don't see how you get that?
Give me a sec
Oh wait.. I was looking at something else. My bad.
Would I use the quadratic formula to find the roots of 3sin^2x−5sinx+1=0?
\[3sinx \times sinx-5\times sinx+\frac{1}{sinx}\times sinx=0 \times sinx\]
yes
\[\frac{ 3\pm \sqrt{5}}{ 2 }\] But then what? I can't isolate for x, can I?
sin x = (3+sqrt5)/2 or sin x = (3-sqrt5)/2
So would I find the arcsin of (3+sqrt5)/2 and (3-sqrt5)/2 for x?
Can't be the first one because sin can't be bigger than 1.
so sin x = .3820
Does there happen to be a way I could solve this without using a calculator?
If you have a table of values you could.
Did you get 22.5 degrees and 157.5 degrees?
Do we need my assistance here or are we ok?

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