  The masses of the $K_1(^3P_1)$ and $K_1(^1P_1)$ are considered in a
nonrelativistic constituent quark model, and the absolute value of the
$K_1(^3P_1)-K_1(^1P_1)$ mixing angle is determined to be about $59.29^\circ$.
Comparison of the theoretical predictions on the strong decay widths of the
$K_1(1270)$ and $K_1(1400)$ in the $^3P_0$ decay model as well as the
production ratio of these two states in the $\tau$ decay between the available
experimental data strongly favors that the $K_1(^3P_1)-K_1(^1P_1)$ mixing angle
is about $+59.29^\circ$.
