If the value of \(\frac{3 \cos 36^{\circ}+5 \sin 18^{\circ}}{5 \cos 36^{\circ}-3 \sin 18^{\circ}}\) is \(\frac{a \sqrt{5…

If the value of \(\frac{3 \cos 36^{\circ}+5 \sin 18^{\circ}}{5 \cos 36^{\circ}-3 \sin 18^{\circ}}\) is \(\frac{a \sqrt{5}-b}{c}\), where \(a, b, c\) are natural numbers and \(\operatorname{gcd}( a , c )=1\), then \(a + b + c\) is equal to :

[JEE Main 2024, 8 Apr (Shift 2)]