Let $\sup,\inf,{\rm dif}$ denote resp supremum , infimum and $\rm dif$ = supremum - infimum.
Does any of the 3 below have a closed form ?
$\sup \Pi_{i=0}^{n} (\sin(i)^2 - \frac{25}{16})$
$\inf \Pi_{i=0}^{n} (\sin(i)^2 - \frac{25}{16})$
${\rm dif} \Pi_{i=0}^{n} (\sin(i)^2 - \frac{25}{16})$