= Solution
Choose all four axes in one plane, at angles
$$
a=0,
\qquad b=0,
\qquad a'=-\frac\pi6,
\qquad b'=\frac\pi6.
$$
Their relevant unsigned separations are
$$
\theta(a,b)=0,
\quad \theta(a,b')=\frac\pi6,
\quad \theta(a',b)=\frac\pi6,
\quad \theta(a',b')=\frac\pi3.
$$
The specified correlation function therefore gives $E(a,b)=E(a,b')=E(a',b)=1$ and $E(a',b')=-1$. Hence
$$
\boxed{E(a,b)+E(a,b')+E(a',b)-E(a',b')=4},
$$
the algebraic maximum and thus a maximal violation of the <CHSH inequality>.
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