Finding all vectors $(x_1, x_2, x_3) \in \mathbb{Z}_{2021^2}^3$ such $x_1x_2x_3 \equiv 43 \;(\text{mod } 2021^2)$

Question

I am trying to find all vectors $(x_1, x_2, x_3) \in \mathbb{Z}_{2021^2}^3$ that satisfies following condition $$x_1x_2x_3 \equiv 43 \;(\text{mod } 2021^2)$$ Since $2021^2 = 43^2 * 47^2$ and $43, 47$ are coprime numbers may be we can use chinese reminder theorem someway?But it's about linear equations, so i have no idea how to move next.