  Histogram Monte Carlo simulation is used to investigate effects of
biquadratic exchange $J_{2}$ on phase transitions of a 3D classical XY
antiferromagnet with frustration induced by the antiferromagnetic exchange
$J_{1}$ and the stacked triangular lattice geometry. The biquadratic exchange
is considered negative (antiferroquadrupolar) within the triangular planes and
positive (ferroquadrupolar) between the planes. The phase diagram obtained
features a variety of interesting phenomena arising from the presence of both
the biquadratic exchange and frustration. In a strong biquadratic exchange
limit ($|J_{1}|/|J_{2}| \leq 0.25$), the antiferroquadrupolar phase transition
which is of second order is followed by the antiferromagnetic one which can be
either first or second order. The separate antiferroquadrupolar and
antiferromagnetic second-order transitions are found to belong to the chiral XY
and Ising universality classes, respectively. If the biquadratic exchange is
reduced both transitions are found to be first order and occur simultaneously
in a wide region of $|J_{1}|/|J_{2}|$. However, if $|J_{2}| \rightarrow 0$ the
transition changes to the second-order one with the chiral universality class
critical behavior.
