Summary: It has been known that finite displacement screws effective for the (incompletely specified) relocation of a body with symmetries form linearly combined sets if they are of a sin-screw form $\widehat{\bold S}=\sin \widehat θ\widehat {\bold s}$, characterised by pitch $P_S=σ/ \tan θ$. Here $\widehat {\bold s}, |\widehat {\bold s}|=1$, is the unit line of the Mozi-Chasles screw-axis, and $\widehatθ=θ+ εσ$ is the dual half-angle of the displacement. This paper shows that screws of a tan-screw form, $\widehat{\bold T}= \tan\widehat θ\widehat {\bold s}$, characterised by pitch $P_T=2 σ/ \sin 2θ$, enjoy the same properties of linear combination.