i need help finding the horizontal tangents on this curve. i got the verticals down correctly, but i cant figure the horizontals out...

C: r=2+2cos(theta)

y=rsin(theta)

y=(2+2cos(theta))sin(theta)

=2sin(theta)+2cos(theta)sin(theta)

dy/d(theta) = 2cos(theta) - 2 sin^2(theta) + 2cos^2(theta)

= 2(cos(theta) - sin^2(theta) + cos^2(theta))

=2(cos(theta) - 1)

2cos(theta) - 2 = 0

2cos(theta) = 2

cos(theta) = 1

(theta) = 0 , 2pi

i was supposed to somehow get pi/3 , 5pi/3 , and pi. where did i go wrong?