Can someone help me with these three pre-calc problems

1. Solve the equation on the interval: 0 (less than or equal to) theta (less than) 2pi
2cos(theta) + 1 = 0

2. Solve the equation on the interval: 0 (less than or equal to) theta (less than) 2pi
cos(theta) = sin 2(theta)

3. Solve the equation on the interval: 0 (less than or equal to) theta (less than) 2pi
2sin^2(theta) + sin(theta)-1=0

Sorry guys if it is confusing but i dont know how to do the symbols on the computer. Also if you could show our every step of your work it would be greatly appreciated as i am still learning.
Thanks!!!!

2cos(t) + 1 = 0
2cos(t) = -1
cos(t) = -1/2
t = 2pi/3 , 4pi/3



cos(t) = sin(2t)
cos(t) = 2 * sin(t) * cos(t)
cos(t) - 2 * sin(t) * cos(t) = 0
cos(t) * (1 - 2sin(t)) = 0

cos(t) = 0
t = pi/2 , 3pi/2

1 - 2sin(t) = 0
1 = 2sin(t)
sin(t) = 1/2
t = pi/6 , 5pi/6

t = pi/6 , pi/2 , 5pi/6 , 3pi/2



2sin(t)^2 + sin(t) - 1 = 0
sin(t) = (-1 +/- sqrt(1 + 8)) / 4
sin(t) = (-1 +/- 3) / 4
sin(t) = -4/4 , 2/4
sin(t) = -1 , 1/2
t = 3pi/2 , pi/6 , 5pi/6