AB = BC and $\angle$ABC=60°. Therefore, ΔABC is an equilateral triangle

Now see that ABOP is a rectangle.

And $\angle$BAN=60°, Therefore, $\angle$NAP=90${}^{\circ }$ − 60${}^{\circ }$ = 30${}^{\circ }$

And $\angle$ANP =$\frac{1}{2}$ * 90 = 45${}^{\circ }$

Now in ΔANP,

$\angle$NPA=180${}^{\circ }$−45${}^{\circ }$−30${}^{\circ }$=105${}^{\circ }$

And hence $\angle$NPO = $\angle$NPA - $\angle$OPA = 105${}^{\circ }$ - 90${}^{\circ }$ = 15${}^{\circ }$

Shortcut

ABC is an equilateral triangle and ABM is a 30 – 60 -90 triangle (M being the point of intersection of AN and the circle). OMN is also 30${}^{\circ }$. MOP = 90${}^{\circ }$, and MNP = 45${}^{\circ }$; MPO = PMO = 45${}^{\circ }$. NPO = 180${}^{\circ }$ – 75${}^{\circ }$ – 45${}^{\circ }$ – 45${}^{\circ }$ = 15${}^{\circ }$