The only expressions that are equal to 4√5 are
2√10
3 × 5^1/2 + 5^1/2
4 × 5^1/2
Given

we have

Squaring both sides, we have

And finally

Note that, when we square both sides, we have to assume that

because we're assuming that this fraction equals a square root, which is positive.
So, if that fraction is positive you'll actually have roots: choose

and you'll have

Which is a valid solution. If, instead, the fraction is negative, you'll have extraneous roots: choose

and you'll have

Squaring both sides (and here's the mistake!!) you'd have

which is not a solution for the equation, if we plug it in we have

Which is clearly false
The answer would be (The two ranges are close together, so there are probably no outliers in this set. )
Just add up all the angles hope you get it right