Trouble with a tangent series expansion

[iatnogpitw]

Okay, so I am supposed to expand ln(cos(x)) basing my calculations on tan(x) = x + (1/3)x^3 + (2/15)x^5 + (17/315)x^7 + ... and expanding out to that fourth term is sufficient. I am having a major brain meltdown, I can't seem to find any equivalencies present, and I'm sure there are. Any help is greatly appreciated.

 

[jostpuur]

Checking what the derivative of the ln(cos(x)) is, should make it evident what is happening.