  Equations of dispersionless Hirota type have been thoroughly investigated in
the mathematical physics and differential geometry literature. It is known that
the parameter space of integrable Hirota type equations in 3D is 21-dimensional
and the action of the natural equivalence group Sp(6, R) on the parameter space
has an open orbit. However the structure of the `master-equation' corresponding
to this orbit remained elusive. Here we prove that the master-equation is
specified by the vanishing of any genus 3 theta constant with even
characteristic. The rich geometry of integrable Hirota type equations sheds new
light on local differential geometry of the genus 3 hyperelliptic divisor, in
particular, the integrability conditions can be viewed as local
differential-geometric constraints that characterise the hyperelliptic divisor
uniquely modulo Sp(6, C)-equivalence.
