summation – Trigonometric Series Function

I came across a function where we have to find n where they give us two separate values a and b.

The function is:

f (n) = 2 x $7^ {n/2} $ x cos(nθ) + n x $4^n$ , where θ = $tan^{-1}$ ($frac32$)

=> the 3 is square rooted in the theta function, I couldn’t figure out how to do that with Math Jax.

The summation is:

$sum_{n=a}^{n=b} f(n)$

With the values of a and b, I need to figure out how to get the value of n given by the function and series.