$m,n$ and $k$ are integers and $9.5\le n\le12$. If
\[
\frac{(\cos\theta+i\sin\theta)^m}
{(\sin\theta+i\cos\theta)^n}
=
k(\sin17\theta-i\cos17\theta),
\]
then $n-m-k=$
Show Hint
Whenever powers of complex trigonometric expressions appear, convert everything into cis form and compare arguments as well as moduli separately.