Short Answer: pi/6 5pi/6 pi/2 3pi/2
Step One
Pull cos(theta) our of the brackets
cos(theta)*(sin(theta) - 1/2) = 0 Do not divide by cos(theta)
Step Two
Identify the sources of the solution
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You have 2 sources of solutions for this
The first is cos(theta)
source 1
cos(theta) = 0
Theta can have 2 values
pi/2 and (3/2 pi)
Source 2
You also have another source
sin(theta - 1/ 2 = 0
sin(theta) = 1/2
Theta can have 2 values One in quadrant 1 and one in quadrant 2
Quadrant 1
Theta = 30o = 30/180 * pi = pi/6
Quadrant 2
Theta = 180 - 30 = 150o = 150o/180 * pi = (5/6) pi
