Is there any known parabolic PDEs in the literature where the angle of analyticity of the associated semigroup is $<\pi/2$ ?

For example, the angle of heat semigroup in Hilbert spaces is exactly $=\pi/2$ (I think this is general for self-adjoint dissipative equations). I'm wondering if there is a known example where the angle is e.g., $\pi/4$ or other value $< \pi/2$.

Is there any known parabolic PDEs in the literature where the angle of analyticity of the associated semigroup is $<\pi/2$ ?

For example, the angle of heat semigroup in $L^2$ is exactly $=\pi/2$. I'm wondering if there is a known example where the angle is e.g., $\pi/4$ or other value $< \pi/2$.