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Dear jauneet singh
here distance form of a line is very helpful
equation of line
(x-1)/ =(y-2)/sinΘ =√6 /3
so x=1+√6 cosΘ /3
and y =2 +√6 sinΘ /3
These point lie on the line x+y =4
so 1+√6 cosΘ /3 +2 +√6 sinΘ /3 =4
or √6 /3 (cosΘ +sinΘ) =1
or 1/√2 (cosΘ +sinΘ) =√3 /2
or sin(Θ+45) =sin 60 or sin 120
for larger angle
sin(Θ+45) =sin 120
Θ=75
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