$$W_t$$ is defined as a wiener process.
How could the expected value of the equation below be calculated on condition that t=1?
$$Y_t = W^2_t * \cos^4(W_t) e^{-\frac32 W^2_t}.$$
At first, I have attempted to simplify the equation partially by getting rid of the biquadratic term $\cos^4(W_t)$ through the $\cos(2x)=2\cos^2(x)-1$ equation but I am unable to relate and proceed further with the rest of the function terms.
An explanatory solution or help will be greatly appreciated since it is significant for me to find a solution at earliest convenience.
Thank you for your assistance.