Solve sin(θ) = x in the range a ≤ θ ≤ b

Mathematica, 60 bytes

NumberForm[t/.NSolve[Sin[t/180Pi]==#&&#2<=t<=#3,{t}],{9,3}]&

input

[0, -1080, 1080]

output

{-1080.000,-900.000,-720.000,-540.000,-360.000,-180.000,0.000,180.000,360.000,540.000,720.000,900.000,1080.000}

Fortran 95 (gfortran), 180 bytes

#define G >=i)write(*,'(f9.3)')
#define H read(*,*)
program a
H x
H i
H j
o=ASIN(x)*57.2957
p=o-180+o
q=o-360*999
do
r=q-p
if(r<=j.and.r G r
if(q>=j)exit
if(q G q
q=q+360
enddo
end

Structure ungolfed:

program a
        implicit none
        real :: x
        integer :: i
        integer :: j
        real :: o
        real :: r
        real :: q
        real :: p

        read(*,*) x
        read(*,*) i
        read(*,*) j

        o=ASIN(x)*57.2957
        p=o-180+o
        q=o-360*999

        do
                r=q-p
                if(r<=j.and.r >=i) then
                        write(*,'(f9.3)') r
                endif
                if(q>=j) then
                        exit
                endif
                if(q >=i) then
                        write(*,'(f9.3)') q
                endif
                q = q + 360
        end do
end program a

APL, 51 46 40 39 bytes

_{3 bytes saved thanks to @KritixiLithos}

_{6 7 bytes saved thanks to @Adám}

{3⍕⍵/⍨1E¯6>|⎕-1○○⍵÷180}⊢+1E3÷⍨(⍳1001×-)

Called as a dyad with a as left argument and b as right argument, prompts for x.

Requires ⎕IO←0.

How?

                         ⊢+1E3÷⍨(⍳1001×-)  ⍝ build the range a to b with step of 0.001
                                  1001×-   ⍝ 1001 * (b - a)
                                 ⍳         ⍝ range
                           1E3÷⍨           ⍝ divide every element by 1000
                         ⊢+                ⍝ add a back

{3⍕⍵/⍨1E¯6>|⎕-1○○⍵÷180}                  ⍝ filter the solutions
                  ○⍵÷180                   ⍝ convert to radian - π * ⍵ / 180
                1○                          ⍝ compute sine
             |⎕-                           ⍝ distance from x
       1E¯6>                                ⍝ small enough
    ⍵/⍨                                    ⍝ compress with the original list
 3⍕                                        ⍝ format to 3 decimal places