在各项均为正数的数列{a_n}中，{S_n}为前n项和，na_n+1²=（n+1）a_n²+a_na_n+1且a₃=π，则tanS₄=____ 

古诗鉴赏，按要求答题。
                                                                                                                              己亥杂诗 龚自珍 清
                                                                                                                  浩荡离愁白日斜，吟鞭东指即天涯。

                                                                                                                  落红不 是无情物，化作春泥更护花。