Adam Meets a Gradient That Flips

Adam keeps two running averages per parameter:

$m_t = \beta_1 m_{t-1} + (1-\beta_1)\,g_t$
$s_t = \beta_2 s_{t-1} + (1-\beta_2)\,g_t^2$
$\theta_{t+1} = \theta_t - \frac{\alpha}{\sqrt{s_t} + \epsilon}\, m_t$

For this problem use $\alpha = 0.05$, $\beta_1 = \beta_2 = 0.9$ (here $\beta_2$ is set to $0.9$ rather than its usual $0.999$ purely to keep the arithmetic light), and $\epsilon = 10^{-8}$, small enough to ignore.

Start from $\theta_0 = 4$ with $m_0 = s_0 = 0$. The parameter is bouncing across a narrow valley, so the first two gradients are equal in size and opposite in sign:

$g_1 = +3, \qquad g_2 = -3$

What is $\theta_2$, to four decimal places?