Maximize does not work


I try to maximise a following function:

 x[t_] :=   1/4 (-1 + a) + a/4 + 1/2 Sqrt[a - a^2] Cos[d] -    1/4 (1 - a) Cos[d + 2*t] + 1/4 a Cos[d - 2*t] +    1/2 Sqrt[a - a^2] Cos[2*t] 

with respect to a and d, and $ t \in (0,\frac{\pi}{4})$ . From NMaximize I know what the range of a and d should be (see figures, where, however, $ t \in (0,\frac{\pi}{2})$ ),

Numerical maximisation with respect to a

Numerical maximisation with respect to d

but I am looking for the analytical formula.

I have written something like this

Maximize[{x[t], 0 < t < Pi/4, 4/5 < a < 1, 0 < d < Pi/2}, {a, d}] 

(I have hoped that limiting the possible values of a and d will help Mathematica), but the output is the same as the input.

Does it mean that the Mathematica is not able to give the analytical form of the maximisation?