I'm confused about how to get the answer of this question.

If cosө=0.2, find the value of:
cosө + cos(ө+2¡Ç) +sin(ө+4¡Ç)

If anyone can help me with this, it would be greatly appreciated.

Some of your symbols didn't translate to ASCII so I'm not sure what the question is. You might need to type the symbols out; use pi for the Greek letter. For angles use A, B and C etc.

You need to tell us tell us what 2¡Ç is. Are you trying to type a Greek character pi? Is the j supposed to be sqrt (-1) ?

If ө is in the first quadrant, ө = 78.46 degrees and sin ө = 0.9798

There are trigonometric identities for sin (A+B) and cos (A+B) that you could use, once you know what 2¡Ç is.