For $0<\alpha\le 1$ and $0<\beta\le 1$, let $K(\alpha,\beta)$ be

the class of normalised close-to-convex

functions defined in the open unit disc $D$ by

$$

\left|\arg\dfrac{zf'(z)}{g(z)}\right|\le\dfrac{\beta\pi}{2} ,

$$

such that $g\in S^{*}(\alpha)$, the class of analytic normalised starlike

functions of order $\alpha$, i.e for $z\in D$,

$$

\left|\arg\dfrac{zg'(z)}{g(z)}\right|\le\dfrac{\alpha\pi}{2}.$$

For $f\in K(\alpha,\beta)$ and given by $f(z)=z+a_{2}z^2+a_{3}z^3+...$, 

sharp bounds are obtained for the Fekete-Szeg\"o functional

$|a_{3}-\mu a_{2}^2|$ when $\mu$ is real.