Step-by-step explanation:tan(β+α) − (3+2√2) tan β = 0Convert to sine and cosine:sin(β+α) / cos(β+α) − (3+2√2) sin β / cos β = 0sin(β+α) / cos(β+α) = (3+2√2) sin β / cos βCross multiply:sin(β+α) cos β = (3+2√2) sin β cos(β+α)sin(2β+α)Rearrange:sin(β+(β+α))Angle sum formula:sin β cos(β+α) + sin(β+α) cos βSubstitute:sin β cos(β+α) + (3+2√2) sin β cos(β+α)(4+2√2) sin β cos(β+α)Rearrange:(2+√2) (2 sin β cos(β+α))Product to sum:(2+√2) (sin(2β+α) + sin(-α))Reflection:(2+√2) (sin(2β+α) − sin α)Since this equals sin(2β+α) from the beginning:(2+√2) (sin(2β+α) − sin α) = sin(2β+α)(2+√2) sin(2β+α) − (2+√2) sin α = sin(2β+α)(1+√2) sin(2β+α) − (2+√2) sin α = 0(1+√2) sin(2β+α) = (2+√2) sin αsin(2β+α) = (2+√2) / (1+√2) sin αMultiply by the conjugate:sin(2β+α) = (2+√2)(1−√2) / ((1+√2)(1−√2)) sin αsin(2β+α) = (2−2√2+√2−2) / (1−√2+√2−2) sin αsin(2β+α) = (-√2) / (-1) sin αsin(2β+α) = √2 sin α