If `csc θ = 3.940`, then `sin theta=1/3.940=0.25381`.

We first find the relevant acute angle.

`α = 0.2566`.

Now θ is in the first and second quadrants because `csc θ` is positive.

So

`θ = 0.2566` (first quadrant), or

`θ = π - 0.2566 = 2.8850` (second quadrant)