\[2\pi\sin\theta\,w(\cos\theta)={\left|\frac{\left({\mathrm{e}}^{2i\theta};q%
\right)_{\infty}}{\left(a{\mathrm{e}}^{\mathrm{i}\theta},b{\mathrm{e}}^{%
\mathrm{i}\theta},c{\mathrm{e}}^{\mathrm{i}\theta},d{\mathrm{e}}^{\mathrm{i}%
\theta};q\right)_{\infty}}\right|}^{2},\]