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Question: How to simplify the following complex matrix product?

Question:How to simplify the following complex matrix product?

_zgj 80 Maple 16
student matrix
March 13 2013
1

T := Typesetting[delayDotProduct](sqrt(2/3), Matrix(3, 3, {(1, 1) = cos(omega*t), (1, 2) = cos(omega*t-(2/3)*Pi), (1, 3) = cos(omega*t+(2/3)*Pi), (2, 1) = -sin(omega*t), (2, 2) = -sin(omega*t-(2/3)*Pi), (2, 3) = -sin(omega*t+(2/3)*Pi), (3, 1) = 1/sqrt(2), (3, 2) = 1/sqrt(2), (3, 3) = 1/sqrt(2)}), true)

To show it clearly,T is shown as left fig.

q:=T*d(transpose(T))/dt

I know the simplified result of "q" is shown as right fig.

but I don't know how to get this result in minimum number of steps in Maple?
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