8. Through the vertex $A$ of a regular tetrahedron $A B C D$, make a section in the shape of an isosceles triangle, and let the angle between the section and the base $B C D$ be $75^{\circ}$. The number of such sections that can be made is $\qquad$.
8. 18 .

Assume the edge length of the regular tetrahedron \(ABCD\) is 1, and the center of the equilateral \(\triangle BCD\) is \(O\).

Within \(\triangle BCD\), a circle is drawn with \(O\) as the center and \(\frac{\sqrt{6}}{3} \cot 75^{\circ}\) as the radius. The intersection of the desired cross-section with the plane \(BCD\) is a tangent to this circle.
We discuss three cases.
(1) When the tangent is parallel to one side of \(\triangle BCD\), there are six such cross-sections;
(2) The tangent \(B_1C_1\) (point \(B_1\) on side \(BC\), point \(C_1\) on side \(CD\)) and \(CB_1 = C_1D\), then the cross-section \(\triangle AB_1C_1\) is an isosceles triangle, and there are six such cross-sections;
(3) Draw a tangent to \(\odot O\) from point \(B\), intersecting \(CD\) at point \(E\). Since \(\triangle BCE \cong \triangle ACE\), we have \(BE = AE\), and thus \(\triangle ABE\) is an isosceles triangle, and there are six such cross-sections. In summary, there are 18 cross-sections that meet the conditions.