You could write the equation of your plane as
This is now in the form ax+by+cz=d. The reason this is helpful is because a normal to the plane written in this form is <a,b,c>. So, you could take your normal vector to be <0.00023, -0.00018, 0.00032>, but the decimals are a bit annoying. So we can scale up by a factor of 10^5 to get the vector <23, -18, 32> that's still normal to the plane and will have the same angle with the xy-plane as <0.00023, -0.00018, 0.00032>, because <23, -18, 32> is parallel to <0.00023, -0.00018, 0.00032>.
Does this help you get started? Good luck!