TeX source:

z_t = w_t +\theta_1 z_{t-1}-\theta^2_1w_{t-2} = w_t + \theta_1z_{t-1} -\theta^2_1(z_{t-2}-\theta_1w_{t-3}) = w_t +\theta_1z_{t-1} -\theta_1^2z_{t-2}+\theta^3_1w_{t-3}