A sphere follows a circular trajectory such that its angular position follows θ(t) = X + Yt - Zt³, where θ is measured in radians, t is measured in seconds, and X, Y, and Z are constants. At t = 0, the angular position of the X is θ = π/3 while the angular velocity is 1.30 rad/s. In another instance, t = 1.80 s, the sphere has an angular acceleration of 0.900 rad/s². At the moment where angular accleration is 2.80 rad/s², determine the values of angular velocity and angular position.