Evaluate the following triple integral by converting it first into spherical coordinates.

${\displaystyle \underset{-1}{\overset{1}{}}}{\displaystyle \underset{0}{\overset{\sqrt[\phantom{2}]{1-y^2}}{}}}{\displaystyle \underset{\sqrt[\phantom{2}]{3x^2+3y^2}}{\overset{\sqrt[\phantom{2}]{7-x^2-y^2}}{}}}18ydzdxdy$