l = 1.45;
\[Tau] = Sqrt[(2*l)/(3*g)];
g = 9.81;

\[Phi]0 = 0.25;
\[Phi]10 = 0;
\[Phi]20 = Sin[\[Phi]0]/\[Tau]^2;

\[Phi][\[CapitalDelta]t_, 
  t_] := \[Phi][
   t] + \[CapitalDelta]t*(\[Phi]1[t] + \[CapitalDelta]t* 
      Sin[\[Phi][t]]/\[Tau]^2)
\[Phi][0] = \[Phi]0;

\[Phi]1[\[CapitalDelta]t_, 
  t_] := \[Phi]1[t] + \[CapitalDelta]t*Sin[\[Phi][t]]/\[Tau]^2
\[Phi]1[0] = \[Phi]10;

\[Phi]2[t_, \[CapitalDelta]t_] := Sin[\[Phi][t]]/\[Tau]^2
\[Phi]2[0] = \[Phi]20;


list = {{0, \[Phi]0, 0}};
\[CapitalDelta]t = 0.001;
t = 0; While[\[Phi][\[CapitalDelta]t, t] <= (Pi/2), 
 list = Append[
   list, {t + \[CapitalDelta]t , \[Phi][\[CapitalDelta]t, t], \[Phi]2[
     t]}]; \[Phi]1[t + \[CapitalDelta]t] = \[Phi]1[\[CapitalDelta]t, 
   t];
  \[Phi][t + \[CapitalDelta]t] = \[Phi][
    t] + \[CapitalDelta]t*\[Phi]1[t + \[CapitalDelta]t];
 \[Phi]2[t + \[CapitalDelta]t] = \[Phi]2[t, \[CapitalDelta]t];
 t = t + \[CapitalDelta]t;]
Last[list]
list