I'm assuming that's a sin²(x), and not a sin(2x), right?
First, collect the terms.
7sin²(x) - 14sin(x) + 7 = 0
Factorise the quadratic.
Due to the high numbers, I'm going to use the quadratic formula to factorise the quadratic.
(-b ± √(b² - 4ac)) / 2a
Therefore
sin(x) = 1
(for both negative and positive of the quadratic formula)
Refer to the quadrant diagram.
sin(x) is a positive, meaning our answer will be on the first and second quadrant.
x = arcsin(1) = 90°
Since you don't provide an interval in your question, I'm going to assume that the interval is 0° ≤ θ ≤ 360°.
Referring again to the quadrant diagram, the solutions are going to be:
θ = 90°, 180°
