In my book it says to choose the ( + or - ) root by observing which quadrant the (sin/cos/tan)/2 of the angle lies.
In the book's example showing the half angle formula, they use sin(105 degrees) = sin(210/2). The sin(105 deg) is positive seeing as it's in the second quadrant.
In this problem (the imgur link above), the sin(u) is negative, and the tan(u) is negative and is in quadrant IV. Why then is the answer utilizing the positive square root when the example and the rule explaining the formula leads me to believe we would be using the negative root?