  For Lebesgue generic $(x_1,x_2)\in \mathbb{R}^2$, we investigate the
distribution of small values of products $q\cdot \|qx_1\| \cdot \|qx_2\|$ with
$q\in\mathbb{N}$, where $\|\cdot \|$ denotes the distance to the closest
integer. The main result gives an asymptotic formula for the number of $1\le
q\le T$ such that $$ a_T <q\cdot \|qx_1\| \cdot \|qx_2\|\leq b_T \quad
\textrm{and} \quad \|qx_1\|, \|qx_2\|\leq c_T $$ for given sequences $a_T,b_T,
c_T$ satisfying certain growth conditions.
