controlling output of a trigonometric sum

Here is a fragment: (the %o lines are messed up)

(%i59)  (t*cos(x)+t^3*cos(3*x))^2*4*cos(x);
                                 3                     2
(%o59)                4 cos(x) (t  cos(3 x) + t cos(x))
(%i60) expand(%);
            6           2           4    2                  2    3
(%o60)   4 t  cos(x) cos (3 x) + 8 t  cos (x) cos(3 x) + 4 t  cos (x)
(%i61) trigreduce(%);
           6             6
          t  cos(7 x)   t  cos(5 x)
          ----------- + -----------    6
               2             2        t  cos(x)
(%o61) 4 (------------------------- + ---------)
                      2                   2
          4             4
         t  cos(5 x)   t  cos(x)
         ----------- + ---------    4                 2               2
              2            2       t  cos(3 x)       t  cos(3 x)   3 t  cos(x)
    + 8 (----------------------- + -----------) + 4 (----------- + -----------)
                    2                   2                 4             4
(%i62) expand(%);
        6             6               4               4             2
(%o62) t  cos(7 x) + t  cos(5 x) + 2 t  cos(5 x) + 4 t  cos(3 x) + t  cos(3 x)
                                           6             4             2
                                      + 2 t  cos(x) + 2 t  cos(x) + 3 t  cos(x)
(%i63) 

I would like the output grouped like this:

cos(x)*(3t^2+2t^4+2t^6) +cos(3x)*(t^2+4t^4) + cos(5x)*(t^6) +cos(&x)*(t^6)

in other words, as a sum of cos(nx)*fn(t). And it would be extra nice if the fn(t) come out in increasing powers of t.

Can this be done?