How many zeroes ? - C

[Camillo]

How many solutions has the equation : \( \displaystyle \frac{{z}}{{4}}+{{\sin}}^{{2}}{z}={0} \) in the (square) domain \( \displaystyle {\left({\left|{R}{e}{z}\right|}\lt{1};{\left|{I}{m}{z}\right|}\lt{1}\right)} \) ?

[Camillo]

Hint : \( \displaystyle {\left|{{\sin}}^{{2}}{z}\right|}={{\sin}}^{{2}}{x}+{{\sinh}}^{{2}}{y} \)