Good one. TAN (the keyword, not the 3 letters) is hex C9 which is also RET in Z80 machine code. The address of the first byte after the keyword in the first statement in a ZX81 program is 16514. USR 16514 calls this address, which immediately returns. The PRINT statement then prints the result of the USR expression, which is the contents of the BC register on return, which I guess happens to contain the start address (since not otherwise set) as a side effect of the implementation.

16509 is the address of the start of the program in memory. Bytes 16509-16510 are the line number (2 byte LSB int). Bytes 16511-16512 are the length of the line. Byte 16513 is the command keyword (REM).