I look carefully at this Plot
Plot[16*80*f^3*3.67*1*108.29^2-1^3/\[Pi]^2*210890*
Coth[(20*1/\[Pi])/(4*f*108.29)]*Sec[0.445457],{f,-.2,.2}]
to estimate locations of solutions.
I then try
FindRoot[16*80*f^3*3.67*1*108.29^2-1^3/\[Pi]^2*210890*
Coth[(20*1/\[Pi])/(4*f*108.29)]*Sec[0.445457]==0,{f,0.175}]
which returns
{f->0.171224}