Could you please specify if you mean 9sin(theta-1) = 7 or 9sin(theta)-1 = 7?

You had:

9sin(θ) - 1 = 7sin(θ)

Subtract 7sin(θ) from both sides:

2sin(θ) - 1 = 0

Now you got:

2sin(θ) = 1

Divide both sides by 2:

sin(θ) = 1/2

Now you’re asking: what values of θ make sin(θ) = 1/2?

Here’s the key bit — we look at the unit circle or our sine knowledge.

Sine equals 1/2 at two standard angles:

• θ = 30° (or π/6 radians)

• and its twin in Quadrant II: θ = 150° (or 5π/6 radians)

So your final answers are:

θ = 30° and θ = 150°
or
θ = π/6 and 5π/6, if you're using radians.

I hope this was the answer you were looking for