Just recall Newton's law of motion:
Recall S = (v + u)*t / 2. .................(1)
Similarly S will be replaced with θ,
v will be replaced with ω
u will be replaced with ω0
Therefore θ = (ω + ω0)*t / 2. .............. (2)
Recall from linear motion v = u + at.
For angular motion it would be ω = ω0 + αt ..............(3)
The linear acceleration a, is replaced with angular acceleration α
Substituting (3) into (2).
θ = ( ω + ω0) * t/2
θ = (ω0 + αt + ω0) *t / 2
θ = (2ω0 + αt) * t/2
θ = (2ω0t + αt^2) /2
θ = (ω0t + 1/2 * αt^2). (Q.E.D)
