PDE with homogeneous boundary conditions in 3D

Question

I'm thinking I need to use Fourier transform but I'm not sure. All I pretty much know Is how to use variable separation but I doubt that will help me with this problem. $$ u_{tt}+au_{t}-c^2(u_{xx}+u_{yy}+u_{zz})=0 $$ $$ x,y,z\in(0,\pi) $$ $$ u(0,y,z,t)=u(\pi,y,z,t)=0 $$ $$ u(x,0,z,t)=u(x,\pi,z,t)=0 $$ $$ u(x,y,0,t)=u(x,y,\pi,t)=0 $$ $$ u(x,y,z,0)=0 $$ $$ u_{t}(x,y,z,0)=sin(x)sin(y)sin^2(z) $$