Reflected line

Geometry Level 5

A ray of light is sent along the line \(2x-3y=5\). After reflecting across the line \(x+y=1\) it enters the opposite side by turning \(15^{o}\) away from the line \(x+y=1\), The slope of line along which the reflected ray travels is

\[ m= \frac{ a \sqrt{b} - c } { d } \]

where \(a,b,c,d\) are co prime natural numbers, and \(b\) is square free.

Find \( a + b + c + d \).


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