Do Italian tourists need a visa if staying in Thailand for less than 30 days and traveling to Manila in between?

Hi guys :)Tourists from Italy dont need a visa to stay in Thailand less than 30 days. I have a return ticket for Bangkok 30th Jan / 14th March. I won't stay 45days in thailand, but i already bought tickets to Manila (10th Feb / 1st March), where i will spend 20 days prior to come back to Bangkok and then leave, so my total stay in Thailand will be less than 30 days. Do i still need a tourist visa? Will my ticket to Manila be valid as proof?

Thanks,

Giorgio