Reviewing on Trigonometry

Just wondering, I was a bit confused on some trigonometry problems when they have a number along with the theta.
For example, what if you have a problem like this:

2csc²Ɵ-8cscƟ+8=1
This is what I did:
1. 2csc²Ɵ-8cscƟ+7=0
Then it looked like a quadratic formula to me.
So I set it up, and in the end, I got csc(Ɵ)=(4+√2)/2, which I got lost because I didn't know what degree that would be.
So I tried turning cscƟ into 1/sinƟ, which then became sinƟ = 2/(4+√2), still a bit lost.

Another example would be: tan(Ɵ+20)=1, I wasn't sure if 20 is a degree or not, since it didn't have a degree thing on top of it.
So what I did was: Ɵ+20=arctan(1), which turns into Ɵ+20 = pi/4, then Ɵ = pi/4 + 20, which I know 45 is pi/4, but not sure what to do with the 20.

So I'm a bit confused with these two, can someone explain?
Thanks :)

In first case you have gone right. just simplify and refer to the tables to get the value of angle. In second case though not mentioned it appears to be degree so treat it as such and proceed further.

Shouldn't there be two solutions to the quadratic equation?

- Hollywood

Of course there would be 2 roots to the quadratic equation 2csc2Ɵ-8cscƟ+7=0 and those would be given by csc(Ɵ)=(4+√2)/2 and csc(Ɵ)=(4-√2)/2,