Algebraically determine the maximum value of the y-coordinate of points on the cardioid for 0 ≤ θ ≤ π.

I used the formula:

, which yielded .

If I solve , setting it to zero, it will give the value of theta at which horizontal tangents exist. The problem is that I don't know how to solve it.

After graphing it, I know that the max value occurs when and , but I'm not sure how to get to those values.