This is the 18299th most frequent Russian word.
широким
"Wide" or "broad" (instrumental case of "широкий").
The word "широким" in this sentence is an adjective in instrumental case modifying the noun "жестом", emphasizing the expressive and expansive nature of the gesture.
Он вышел на дорогу с широким жестом.
He stepped onto the road with a wide gesture.
The word "широким" is used as an adjective in instrumental case describing "спектром", illustrating the diverse and comprehensive collection of ideas.
Поделись широким спектром своих идей.
Share a wide range of your ideas.
Here, "широкий" appears in nominative form correlating with "подход", highlighting the inclusive and far-reaching methodology being referred to.