.

$\displaystyle { \left[{\bf X}({\bf X}'{\bf X})^{-1}{\bf C}'\left[ {\bf C}({\bf ... ...} \right]^{-1}(\boldsymbol{\theta} - {\bf C}\hat{\boldsymbol{\beta}}) \right] }$
	$\displaystyle =$	$\displaystyle (\boldsymbol{\theta} - {\bf C}\hat{\boldsymbol{\beta}})' \left[ {... ...-1}{\bf C} \right]^{-1} (\boldsymbol{\theta} - {\bf C}\hat{\boldsymbol{\beta}})$
	$\displaystyle =$	$\displaystyle (\boldsymbol{\theta} - {\bf C}\hat{\boldsymbol{\beta}})' \left[ {... ...-1}{\bf C} \right]^{-1} (\boldsymbol{\theta} - {\bf C}\hat{\boldsymbol{\beta}})$
	$\displaystyle =$	$\displaystyle (\boldsymbol{\theta} - {\bf C}\hat{\boldsymbol{\beta}})' \left[ {... ...-1}{\bf C} \right]^{-1} (\boldsymbol{\theta} - {\bf C}\hat{\boldsymbol{\beta}})$