Partial fraction expansion of $\pi^2/\sin^2\pi z$

Show that \({ \frac { \pi ^ { 2 } } { \sin ^ { 2 } \pi z } } \operatorname { a n d } g ( z ) = \sum _ { n = - \infty } ^ { \infty } { \frac { 1 } { ( z - n ) ^ { 2 } } }\) have the same principal part at each integer point.

Show that \(h ( z ) ~ = ~ \frac { \pi ^ { 2 } } { \sin ^ { 2 } \pi z } - g ( z )\) is bounded on C and conclude that \(\frac { \pi ^ { 2 } } { \sin ^ { 2 } \pi z } =\) \(\sum _ { n = - \infty } ^ { \infty } \frac { 1 } { ( z - n ) ^ { 2 } } .\)