Why does NMaxmize miss this true maximum?


I am having trouble with maximizing a function which appears as a curvature of a planar curve.

{tmin, tmax} = {0, 2 Pi}  f=-((6-3 Cos[t]-Cos[3 t])/((-11+6 Cos[t]+8 Cos[2 t]-6 Cos[3 t]+Cos[4 t])   Sqrt[Cos[t]^2+9 Sin[t]^2-12 Cos[t] Sin[t]^2+4 Cos[t]^2 Sin[t]^2]));  NMaximize[{f, tmin <= t <= tmax}, t] 

says that the maximum of f is attained at

{1.37888, {t -> 5.78352}} 

But,

Plot[f, {t, tmin, tmax}, PlotRange -> Full] 

plot of f

indicates that the true maximum is attained at t=Pi

Why is this happening? I’m using Mathematica version 12.0.0 for Microsoft Windows (64-bit).