(I'm going to replace theta with "x" for efficiency purposes)
You can factor out a tanx to get:
Tanx(2cosx+1) = 0
Now set each part equal to 0 to find answers:
Tanx=0
X= pi and 2pi
Now second part:
2cosx+1=0
2cosx = -1
Cosx= -1/2
X= 2pi/3 and 4pi/3
So your answer is:
X= pi, 2pi, 2pi/3, and 4pi/3
I hope this Helps!
