# Alternate Frame Ticks, Only Label Specific Ones [closed]

I have the following function that I would like to plot:

g1[x_, t_] := Tan[x]*Sin[2 Pi t] + Cot[x]*Cos[2 Pi t];
rs1 := {x, -2 \[Pi], 2 \[Pi]};
rx1 := {-2 \[Pi], 2 \[Pi]};
ry1 := rx1;
b = rx1[] - rx1[];
b1 = Table[i*b/8 + rx1[], {i, 7}]

Plot[g1[x, 0.01], Evaluate[rs1], PlotRange -> {rx1, ry1},
PlotStyle -> {Purple}, Axes -> False, AspectRatio -> Automatic,
Frame -> True, FrameTicks -> {b1, b1}, FrameStyle -> White,
FrameTicksStyle -> Black] This is very close to what I want, but I want the labeled tick marks to be longer and I want shorter ones in between (with no corresponding number next to them). So, for example, there should be another black tick in between 0 and pi/2, pi/2 and pi, pi and 3pi/2, and one after 3pi/2, and repeated on the negative side, and they should have no numbers. But that's all.

I drew on the image to make it easier to see where I want those smaller tick marks. How would I do that?

ticks = Subdivide[## & @@ Rest@rs1, 8];
minorticks = Thread[{MovingAverage[ticks, 2], "", {0, .02}}, List, 1];
majorticks = Thread[{Rest@Most@ticks, Rest@Most@ticks, {0, 0.03}}, List, 2];

Plot[g1[x, 0.01], Evaluate[rs1], PlotRange -> {rx1, ry1},
PlotStyle -> {Purple}, Axes -> False, AspectRatio -> Automatic,
Frame -> True,
FrameTicks -> {Join[majorticks, minorticks], Join[majorticks, minorticks]},
FrameStyle -> White,
FrameTicksStyle -> Black] 