Linear Model Problem

I am working on a linear model problem.

Here is the model:

Wi = a*Zi + b*Zi*Xi + Zi*Ei

Wi is the observed response. a and b are the regression
coefficients. Zi follows a Beta distribution with parameters alpha and
beta (they are both unknown). Xi is a predictor variable, and Ei is
the error with mean zero and variance sigma^2.

I need to estimate a, b, alpha, beta, and sigma^2 using method of
moments. I want formulas for them. I've never seen a linear model like
this before and have no idea how to tackle it. Any help or hints would
be greatly appreciated. Thanks in advance.

.

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