Use trigonometric identities to solve 2cos22sin2220 exactly

Use trigonometric identities to solve 2cos2()+2sin2(/2)2=0 exactly for 0<2. If there is more than one answer, enter your answers as a comma separated list.

the first answer is 0, i know that much. but the second answer is NOT pi and I have no idea what the thrid and fourth answers are.

Solution

2cos²theta +2sin(theta/2)-2=0

2cos²theta + 1 -cos theta -2=0

2cos²theta -cos theta -1=0

2cos ²theta -2 cos theta + cos theta -1=0

2cos theta(cos theta-1)+1(cos theta-1)=0

(2 cos theta +1)(cos theta-1)=0

cos theta=-1/2, cos theta=1

theta=2pi/3, 4pi/3, 0

theta=0, 2pi/3,3pi/2, 4pi/3