The most general value of $\theta$ which satisfy both the  equations $\cos \theta =-\frac{1}{\sqrt{2}}$ and $\tan \theta =1$, is

The values of $\theta$satisfying $\cos \theta =-\frac{1}{\sqrt{2}}$ and lying between 0 and $2\mathrm{\pi }$ are $\frac{3\pi }{4},\frac{5\pi }{4}$ 

Similarly, the values of $\theta$, lying between 0 and $2\mathrm{\pi }$, satisfying  $\tan \theta =1$ are $\frac{\pi }{4},\frac{5\pi }{4}$.

Thus, the value of $\theta$ between 0 and $2\mathrm{\pi }$ which satisfies both the equations is $\frac{5\mathrm{\pi }}{4}$.

Hence, the general value of $\theta$ is $2n\pi +\frac{5\pi }{4},n\in Z$