Restart;
DeclareTriads[a,b];
DefineTriads[a,b,theta,3];
w=MakeTranslations[{a,1},{b,-Cos[theta],Sin[theta],0}];
MamboExpress[w,a]

$\left\{''Type''\to ''Vector'',''Size''\to 1,1\to \left\{''Coordinates''\to \left\{1-{\mathrm{Cos}\left[\mathrm{theta}\right]}^2-{\mathrm{Sin}\left[\mathrm{theta}\right]}^2,0,0\right\},''Triad''\to a\right\}\right\}$

MamboSimplify[%]

$\left\{''Type''\to ''Vector'',''Size''\to 0\right\}$