V   =  100;
nn  =  10;
x0  =  -(π/2);
x1  =  -(π/2);

\(ts\  = \ η /. 
        Table[
	x0 = i\ π\ ; \ 
          x1 = Min[x0\  + \ π/2, \@V]; 
          xm\  = \ \(x0 + x1\)\/2; 
	 (*Print[
              x0, "  ", xm, "  ", x1]*) 
	
          gg = FindRoot[
              Tan[η]\  == \@\(V - η\^2\)\/η, {η, 
                xm, x0, x1}]
	, {i, 0, 
            Floor[\@V\/π]}]

\ \)
\(ta\  = η /. \ 
        Table[
	x0 = \((i\  + 1/2)\) π; \ 
          x1 = \ Min[x1 + π, \@V]; 
          xm\  = \ \(x0 + x1\)\/2; 
	 (*\(Print[
                x0, "  ", xm, "  ", x1];\)*) 
	
          FindRoot[
            Tan[η]\  == \(-\(η\/\@\(V - η\)\)\), {η, xm, x0, x1}]
	, {i, 0, 
            Floor[\@V\/π - 1\/2]}]\)