proove that 
tan22 + tan23 +tan22tan23 = 1

tan22 + tan23 + tan22.tan23  = 1
=tan(22+23)[1- tan22.tan23] + tan22.tan23 
=tan 45 [ 1- tan22.tan23 ] + tan22.tan23
=1- tan22.tan23+tan22.tan23
=1