Question Number 191229 by mr W last updated on 22/Apr/23
$${evaluate} \\ $$$${P}_{{n}} =\left({a}+\mathrm{sin}\:\theta\right)\left({a}+\mathrm{sin}\:\frac{\theta}{\mathrm{2}}\right)\left({a}+\mathrm{sin}\:\frac{\theta}{\mathrm{2}^{\mathrm{2}} }\right)…\left({a}+\mathrm{sin}\:\frac{\theta}{\mathrm{2}^{{n}} }\right) \\ $$$${with}\:\mid{a}\mid\leqslant\mathrm{1} \\ $$