Matrix of a composition of a spatial rotation and reflection

Let \(T:\mathbb R^3\to\mathbb R^3\) be the rotation by \(60^\circ\) counterclockwise in the plane perpendicular to \((1,1,1)\), and let \(S:\mathbb R^3\to\mathbb R^3\) be reflection in the plane perpendicular to \((1,0,1)\). Determine the matrix of \(S\circ T\) in the standard basis \[ \{(1,0,0),(0,1,0),(0,0,1)\}. \] You do not have to multiply the resulting matrices, but you must determine any inverses that arise.