SIT Technique
$\mathbb{E}_x[X] = \mathbb{E}_y [\mathbb{E}[X|Y]]$
$\mathbb{E}[g(x,~y,~z)] = \mathbb{E}z [\mathbb{E}{y|z}[ \mathbb{E}_{x|y,z}[g(x,~y,~z)|y,~z]]]$
$\mathbb{E}_x[X] = \mathbb{E}_y [\mathbb{E}[X|Y]]$
$\mathbb{E}[g(x,~y,~z)] = \mathbb{E}z [\mathbb{E}{y|z}[ \mathbb{E}_{x|y,z}[g(x,~y,~z)|y,~z]]]$