My theory:
The ethyl groups in diethylether being larger in size when compared to hydrogens in water, should be repelled more by the lone pairs on the central atom oxygen. Hence, the ethyl groups should come closer, thereby decreasing the bond angle.
Moreover, the electronegativity difference between the central atom and the peripheral atoms is more in case of water i.e., $\ce{O-H}$ electronegativity difference is more than that in $\ce{C-O}$ as per Pauling’s scale. Hence, the oxygen atom should pull the bond pair closer, thereby allowing to open up the $\ce{H-O-H}$ bond increasing the bond angle.
Hence bond angle of water should be greater than that of diethylether. Am I right?
PS: I know that in reality dimethylether has greater bond angle than water.