Verified answer

4cos(2Ɵ)=-4cosƟ__________(1)

remember that cos 2Ɵ = 2cos²Ɵ - 1

eq .1 rewrite become

8cos²Ɵ - 4 = 4cosƟ

8cos²Ɵ - 4cosƟ - 4 = 0

2cos²Ɵ - cosƟ - 1 = 0

(2cosƟ + 1)(cosƟ - 1) = 0

(2cosƟ + 1) = 0

cosƟ = -1/2 --> (Ɵ = 120;240)

or

(cosƟ - 1) = 0

cosƟ = 1-->(Ɵ= 0;360)

Ɵ = 0;120;240;360

SOLVED

π/3, π

120 and 240 do not work. That person did something wrong. I'm staring straight at a unit circle.

cos 120 = -1/2

cos 2(120) = -1/2

4(-1/2) does not equal -4(-1/2)

Also, 0 and 360 do not work since they are not included in your specified interval. You specified greater than zero and less than 360. not greater than or equal to and less than or equal to. That person's answer is completely wrong.

It is 60deg(pi/3) or 180deg(pi)