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Nice tutorial but there is one big mistake.The Arduino can NOT supply enough power to the ESP8266 when it is transmitting.Use a 5V to 3.3 V regulator to power the ESP8266. Also put 100 microfarad + 100nF across3.3 V to filter the power supply.
Very good job to cram so much in just 8k memory.Have you considered to upgrade to the Attiny167 ? 16k memory.Who supplied the 8 pin programming clip ? Price ?
Why bother to struggle with pin numbers, libraries and different versions of the Arduino IDE ?There are so many incompatibility issues here with the Tiny chips.This combo works: Arduino 1.8.5 and AttinyCore. On Ebay you can buy Arduino Pro Mini for £ 1.44 with header pins including shipping. How much is your sparetime worth ?Yes, I have been there. All the way with tiny13A,45,84,85.,88.Buy some Pro Mini 3 Volts @8 MHz also so you dont have to worry with voltage dividerswhen using displays,sensors etc from the cell phone industry running at 3.3 volts max.Don't even try to use 5 volts on a 3.3 V device. It will break.