We willl very happy to play basketball. 这里的to play basketbal

宾语.
We will be very happy to play basketball与We will be very happy that we can play basketball after school.的句型结构是一样的,只不过前者是动词不定式,后者是从句.
我们知道,有三种词可以带宾语：一是及物动词,二是介词,三是happy,sorry,afraid,sad,glad,disappointed等表示情感的形容词,这种形容词后面可以带that引导的宾语从句.又如：
I'm glad that you can come.很高兴你能来.
我们也知道,如果从句的主语与主句的主语相同时,常常可以将宾语从句改成to do短语.
不明白的再问哟!请记得采纳,多谢!