What are the momentum and energy of a photon of wavelength $\lambda$ ?

A photon of wavelength $\lambda$ is incident on an electron. After the collision, the photon has wavelength $\lambda^{\prime}$. Show that

$$\lambda^{\prime}-\lambda=\frac{h}{m c}(1-\cos \theta),$$

where $\theta$ is the scattering angle and $m$ is the electron rest mass.