ListDensityPlot bounded by a region

I want to make a ListDensityPlot within the region bounded by

ImplicitRegion[
Abs[x] <= (2 \[Pi])/Sqrt[3] && Abs[-(x/Sqrt[3]) + y] <= (4 \[Pi])/3 &&
Abs[x/Sqrt[3] + y] <= (4 \[Pi])/3, {x, y}]


amp = Import[
"ssf_ud01_249.dat",
"Table"];
a = ListDensityPlot[amp, Frame -> True,
FrameTicksStyle -> Directive[Black, 18], FrameLabel -> {"", ""},
FrameStyle ->
Directive[Black, FontSize -> 22, FontFamily -> "Times"],
PlotLegends -> Placed[Automatic, Right],
LabelStyle ->
Directive[Black, FontSize -> 16, FontFamily -> "Times"],
ColorFunction -> (ColorData["BlueGreenYellow"][
Rescale[#, {-0.05, 1.05}]] &), ColorFunctionScaling -> True,
PlotRange -> {{(-2 \[Pi])/Sqrt[3], (2 \[Pi])/Sqrt[3]}, {(-4 \[Pi])/
3, (4 \[Pi])/3}, All}, AspectRatio -> 2/Sqrt[3]];

g2 = Graphics[{Black, Thickness[0.005],
Line[{{0, (4 \[Pi])/3}, {-((2 \[Pi])/Sqrt[3]), (2 \[Pi])/
3}, {-((2 \[Pi])/Sqrt[3]), -((2 \[Pi])/3)}, {0, -((4 \[Pi])/
3)}, {(2 \[Pi])/Sqrt[3], -((2 \[Pi])/3)}, {(2 \[Pi])/Sqrt[
3], (2 \[Pi])/3}, {0, (4 \[Pi])/3}}]}];
Show[a, g2]


Can anyone help me in this case? Thank you in advance.

Defined a RegionFunction, Function[{x, y}, rm@{x, y} where rm = RegionMember[reg].

Clear[reg,rm];
reg = ImplicitRegion[
Abs[x] <= (2 π)/Sqrt[3] &&
Abs[-(x/Sqrt[3]) + y] <= (4 π)/3 &&
Abs[x/Sqrt[3] + y] <= (4 π)/3, {x, y}];

rm = RegionMember[reg];

ListDensityPlot[amp, Frame -> True,
FrameTicksStyle -> Directive[Black, 18], FrameLabel -> {"", ""},
FrameStyle ->
Directive[Black, FontSize -> 22, FontFamily -> "Times"],
PlotLegends -> Placed[Automatic, Right],
LabelStyle ->
Directive[Black, FontSize -> 16, FontFamily -> "Times"],
ColorFunction -> (ColorData["BlueGreenYellow"][
Rescale[#, {-0.05, 1.05}]] &), ColorFunctionScaling -> True,
PlotRange -> {{(-2 π)/Sqrt[3], (2 π)/Sqrt[3]}, {(-4 π)/
3, (4 π)/3}, All}, AspectRatio -> 2/Sqrt[3],
RegionFunction -> Function[{x, y}, rm@{x, y}]]