I'm trying solve this problem using matlab, anybody know good strategies to work with system of trigonometric inequalities such as
$ \left[\exp(-q_1*i)\cos^3(p_3)\sin(p_1)\sin(p_2)\sin(p_3)\right]\cdot a - \left[\exp(-q_2i)\exp(-q_3i)\cos(p_1)\cos(p_2)\cos^2(p_3)\sin(p_2)\sin^2(p_3) \right]\cdot b \neq 0,$
where $a$ and $b$ are complex variables and $q_{i}$ and $p_{i}$ are real variables. The real system (the least of them) have 18 inequalities and 8 variables, I need know if there is a set of values (8 real values) that makes true at least one of the inequalities. Maybe a good path is know how determine the minimum value of a expression of type
$\left[\exp(a_1i)\cos^3(a_2)\sin(a_3)\sin(a_4)\sin^2(a_5)\right]$,
or a bit more complex like
$\left[\exp(a_1i)\cos^3(a_2)\sin(a_3)\sin(a_4)\sin^2(a_5)\right] \cdot \left[\exp(-b_1i)\cos^2(b_2)\sin(b_3)\sin(b_4)\sin^3(b_5)\right].$
Then, some idea?