Given that $$(1+\sin t)(1+\cos t)=5/4$$ and $$(1-\sin t)(1-\cos t)=\frac mn-\sqrt{k},$$ where $$k, m,$$ and $$n_{}$$ are positive integers with $$m_{}$$ and $$n_{}$$ relatively prime, find $$k+m+n.$$

(第十三届AIME1995 第7题)