find 4 solutions of the equation
(sinx)2 = 1/4 for x between 0degrees and 360degrees..
This isn't a sine rule question... but I'll solve it...
$\displaystyle \sin^2{x} = \frac{1}{4}$
$\displaystyle \sin{x} = \pm \frac{1}{2}$
So we need to figure out which $\displaystyle x$ satisfy this equation.
The focus angle is $\displaystyle 30^{\circ}$.
In each of the other quadrants, the angles that satisfy this equation are
$\displaystyle 180^{\circ} - 30^{\circ}, 180^{\circ} + 30^{\circ}, 360^{\circ} - 30^{\circ}$.
So the four angles are $\displaystyle \left\{30^{\circ}, 150^{\circ}, 210^{\circ}, 330^{\circ}\right\}$.