Session p. 177

θ[q_Real] := 
      2  (q^(1/4)) 
        NSum[((((-1))^k)/(2  k + 1)) (q^(k (k + 1))), {k, 
            0, ∞}]
\(\(t\_*\) == \((t /. 
          FindRoot[θ[E\^\(\(-π\^2\) t\)] == π\/\(2 \@ 5\), {t, 0.4, 0.5}, 
            AccuracyGoal -> MachinePrecision])\)\)