sol = Solve[
         4*Sin[a/2]*Cos[a/2]^3*tr + Sin[a/2] == 1 && 0 <= a <= Pi, {a, tr}, 
          Reals]

    (*   {{a -> \[Pi]}, {tr -> 
           ConditionalExpression[1/4 Csc[a/2] Sec[a/2]^3 (1 - Sin[a/2]), 
            0 < a < \[Pi]]}}   *)

    Plot[Evaluate[tr /. sol], {a, 0, Pi}, PlotRange -> {0, 20}, 
         GridLines -> Automatic]