  In this manuscript we study the counting problem for harmonic trinomials of
the form $a\zeta^n+b\overline{\zeta}^m+c$, where $n,m\in \mathbb{N}$, $n>m$,
and $a$, $b$ and $c$ are non-zero complex numbers. As a consequence, we obtain
the Fundamental Theorem of Algebra and the Wilmshurst conjecture for harmonic
trinomials. The proof of the counting problem relies on the Bohl method
introduced in Bohl (1908).
