question involving einstein and taylor series calculus 2?

Question

question i am working on for hw reads as follows

One of Einstein;s most amazing predictions was that light traveling from distant stars would bend around the sun on the way to earth. His calculations involved solving for θ in the equation

sinθ + b(1+cos^2 θ + cosθ) = 0

where b is a very small positive constant.

Question: Expand the left-hand side of the equation in Taylor Series about θ = 0 , disregarding terms of order θ^2 and higher. (Your answer will involve b)

I am very stuck on this question, any help would be appreciated.

Answer 1

They want you to approximate the function
f(θ) = sinθ + b(1+cos^2 θ + cosθ) using the first two terms of the Taylor's series. You only need the first two terms because the 3rd term involves θ^2.
The first term of the Taylor's series is just f(0)
The second term will be f'(0) times θ. So find the derivative of f(x) then evaluate it at x = 0.