I am trying to calculate **analytic** solution (or *locus*) of *zeros* of a very large **multi-variable** function which is consisted of thousands of **nonlinear trigonometric** terms. All the variables are **real numbers**. The function **is not differential**.

(The equation is a *Singular Value* of the *constrains matrix* of a mechanical system)

Here is an example of what I want:

For this equation: $$ f = y\sin(\theta) - z\cos(\theta) $$ Where $ \theta,y,z \in \mathbb{R} $ (and if it helps: $ 0 \le \theta < 2\pi$).

I want all the sets of **real** values of $\theta$, $y$ and $z$ that satisfy $f = 0$, which would be the following three set of answers:

$$ \theta = \arctan(\frac{z}{y}) $$

$$ z = 0,\ \theta = \{0,...\},\ y\in \mathbb{R} $$

$$ y = 0,\ \theta = \{\pi/2,...\},\ z\in \mathbb{R} $$

**Q**: Is there any way in any software that this solution could be achieved?

Any help would be much appreciated! Thanks.