Let SABC be a regular triangular pyramid. Find the set of all points $ D (D! = S)$ in the space satisfing the equation $ |cos ASD - 2cosBSD - 2 cos CSD| = 3$.
a better restatement of the problem
Let ${SABC}$. be a regular triangular pyramid (${SA=SB=SC}$. and ${AB=BC=CA)}$ ). Find the locus of all points ${D \, (D\ne S)}$. in the space that satisfy the equation ${ |cos \delta_A -2cos \delta_B - 2cos \delta_C | = 3 }$. where the angle ${\delta_X=\angle XSD}$ for each ${X \in \{ A,B,C\} }$.