I have no choice but to do it.

这涉及but加动词不定式的用法.
当不定式结构作 but（except,besides） 等介词的宾语,且 but（except,besides） 等词前面的句中有实意动词 do 时,该不定式结构中的 to 要省略,否则一般不省略.
例如：
1.We have no choice but to arrive late.除了迟到以外,我们并无选择.
2.We have no choice but to turn back.没办法,我们只有回去.
3.You have no choice but to give up.你别无选择,只能投降.
4.At present I can do nothing but wait.目前,我只好等待.
5.He can do nothing but lie down and sleep.他无事可做只好躺下睡觉.
6.You can do nothing but let matter take their course.你无能为力,只能听其自然.