[LaTeX] "Runaway argument" in environment multline

[dydale]

Mi potete aiutare a trovare cosa non va un questo codice

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{multline*}
sin^{2}z+cos^{2}z=\left(\frac{e^{iz}-e^{-iz}}{2i}\right)^{2}+ \left(\frac{e^{iz}-e^{-iz}}{2}\right)^{2}\\
=-\frac{left(e^{iz}-e^{-iz}\right)^{2}}{4}+\frac{\left(e^{iz}-e^{-iz}\right)^{2}{4}=\frac{\left(e^{iz}+e^{-iz}\right)^{2}-\left(e^{iz}-e^{-iz}\right)^{2}{4}=\frac{[\left(e^{iz}+e^{-iz}\right)-\left(e^{iz}+e^{-iz}\right)][\left(e^{iz}+e^{-iz}\right)+\left(e^{iz}+e^{-iz}\right)]}{4}\\
=\frac{\left(2e^{-iz}\right) \left(2e^{iz}\right)}{4}=\frac{4e^{0}}{4}=1
\end{multline*}
\end{document}

L'errore è:
Runaway argument?
sin^{2}z+cos^{2}z=\left (\frac {e^{iz}-e^{-iz}}{2i}\right )^{2}+ \left \ETC.
! File ended while scanning use of \multline*.
<inserted text>

! Missing $ inserted.
<inserted text>
$

! Missing \endgroup inserted.
<inserted text>
\endgroup

! Display math should end with $$.
<to be read again>

Dovrebbe venire così:
Latex_equ2.jpg

Grazie.