# How to remove an unwanted line-like disruption with jagged edges in Plot3D?

I'm trying to plot a function that doesn't have singular points, but the output displays a line-like disruption where the graph appears discontinuous. My code is here, and the output follows.

c = 2.78; q = 0.16; x0 = -2;
setting1 = {ClippingStyle -> None, ColorFunction -> "Rainbow",
Exclusions -> "Singularities", PlotRange -> Automatic,
PlotStyle -> Directive[Opacity[0.8], Thick, Red]};
Plot3D[
-((Sqrt[c/q] (1 - Tan[1/2 Sqrt[c/q] (-c t + x + x0)]))/(
2 (1 + Tan[1/2 Sqrt[c/q] (-c t + x + x0)]))) + (
c (1 + Tan[1/2 Sqrt[c/q] (-c t + x + x0)]))/(
2 Sqrt[c/q] q (1 - Tan[1/2 Sqrt[c/q] (-c t + x + x0)]))
, {x, -2, 2}, {t, 0.1, 1},
Evaluate[setting1],
AxesLabel -> {"x", "t", "U", " "},
PlotLabel -> "U"]


Upon setting Exclusions to 'None' these disruptions disappear. However, singular points then emerge in the form of pillars, which are also visually bad.

So my question is, how to avoid these disruptions without showing singular points? I tried to set MaxRecursion and PlotPoints but it did not work.

Your function $$-\frac{2 \sqrt{\frac{c}{q}} \tan \left(\frac{1}{2} \sqrt{\frac{c}{q}} (-c t+x+\text{x0})\right)}{\tan ^2\left(\frac{1}{2} \sqrt{\frac{c}{q}} (-c t+x+\text{x0})\right)-1}$$ is singulaer if

 1/2 Sqrt[c/q] (x - c t + x0) == Pi/4 (2 k - 1), Element[k,Integers]

c = 2.78; q = 0.16; x0 = -2;
setting1 = {ClippingStyle -> None, ColorFunction -> "Rainbow",
Exclusions ->
Table[ 1/2 Sqrt[c/q] (x - c t + x0) == Pi/4 (2 k - 1) , {k, -10,
10}]  , PlotRange -> Automatic,
PlotStyle -> Directive[Opacity[0.8], Thick, Red]};
Plot3D[-((Sqrt[
c/q] (1 - Tan[1/2 Sqrt[c/q] (-c t + x + x0)]))/(2 (1 +
Tan[1/2 Sqrt[c/q] (-c t + x + x0)]))) + (c (1 +
Tan[1/2 Sqrt[c/q] (-c t + x + x0)]))/(2 Sqrt[
c/q] q (1 - Tan[1/2 Sqrt[c/q] (-c t + x + x0)])), {x, -2,
2}, {t, 0.1, 1}, Evaluate[setting1],
AxesLabel -> {"x", "t", "U", " "}, PlotLabel -> "U"
]