In my textbook of trigonometry there is, for an exercise, a misprint (fix typo) on this equation $$3\sin ^2\left(x\right)-\sqrt{3}\color{red}{\sin \left(\cos \left(x\right)\right)}+3\sin \left(2x\right)-2\sqrt{3}\cos ^2\left(x\right)=0 \tag1$$ because it is missed the $x$ for the operator $\sin$. Here there is the original photo:
I believe that with derivatives or numerical methods can be solved the $(1)$. Is there no hope of being able to find the solution in case there is a misprint like this?
In general, equations like that (without the correction) are pretty much hopeless to solve, except that sometimes you get lucky, and say 'suppose $\cos x = 0$...', then $\sin x = \pm1$, and the $\sin \cos x$ term goes away completely, and it turns out that everything else works fine when $\sin x = +1$, say...but that's just blind luck.
You can also write out the whole mess with Taylor series and hope to get some sort of recurrence you can solve.. .but it's a long shot.