Large Scale Central

A question for the engineering type folks

This is a goofy engineering/architectural question for a project I am building here at home.

I want to build a “sun trellis” over my patio deck. The ceiling joist are running at about 46 degrees East off that side of my home. I live at about 40.5 degrees latitude.

I want to install 3.5" (89 mm) slats to shield the sun in the summer months and permit sun to warm the area in the winter.

What I need are the degrees of angles north to south for the slats and the deviation off vertical to accomplish this.